Exam 1

A boy throws a rock with an initial velocity of 3.13 m/s at 30.0 degrees above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory?

vy = 3.13 m/s *sin(30)=1.57 m/s the time to reach the max height t is: t = vy/g = 1.57m/s / 9.8m/s2 = 0.16s

An apple falls from a tree and hits the ground 5 meters below with a speed of about

10 m/s

The United States is about the only country that still uses the units feet, miles, and gallons. However, you might see some car specifications that give fuel efficiency as 7.6 km per kilogram of fuel. Given that a mile is 1.609 km, a gallon is 3.785 liters, and a liter of gasoline has a mass of 0.729 kg, what is the car's fuel efficiency in miles per gallon?

13 mpg

A student wants to determine the distance from the lakeshore to a small island. He first draws a 50-m line parallel to the shore. Then, he goes to the ends of the line and measures the angles of the lines of sight from the island relative to the line he has drawn. The angles are 30◦ and 40◦ . How far is the island from the shore?

17 m

Figure shows the position-versus-time graphs for two objects, A and B, that are moving along the same axis. (a) At the instant t = 1 s, is the speed of A greater than, less than, or equal to the speed of B? Explain. (b) Do objects A and B ever have the same speed? If so, at what time or times? Explain.

(a) A's speed is greater at t = 1 s. The slope of the tangent to B's curve at t = 1 s is smaller than the slope of A's line. (b) A and B have the same speed just before t = 3 s. At that time, the slope of the tangent to the curve representing B's motion is equal to the slope of the line representing A's motion.

Figure gives the position-versus-time graph of a car. (a) Draw the car's velocity-versus-time graph. (b) Describe the car's motion in words.

(a) From t = 0 to t = 2 s (∆t = 2 s) the car's displacement is ∆x = −4−0 = −4 m, so the velocity during this time interval: v = ∆x ∆t = −4 2 = −2 m/s From t = 2 to t = 4 s, the car's position does not change (∆x = 0 m), so v = 0 m/s. From t = 4 to t = 6 s, the car's displacement is ∆x = 10 m, so the velocity during this time interval: v = 10 2 = 5 m/s (b) The car backs up for 2 s at 2 m/s, sits at rest for 2 s, then drives forward at 5 m/s for 2 s.

Figure shows an object's position-versus-time graph. The letters A to E correspond to various segments of the motion in which the graph has constant slope. (a) Write a realistic motion short story for an object that would have this position graph. (b) In which segment(s) is the object at rest? (c) In which segment(s) is the object moving to the right? (d) Is the speed of the object during segment C greater than, equal to, or less than its speed during segment E? Explain.

(a) Sirius the dog starts at about 1 m west of a fire hydrant (the hydrant is the x = 0 m position) and walks toward the east at a constant speed, passing the hydrant at t = 1.5 s. At t = 4 s Sirius encounters his faithful friend Fido 2 m east of the hydrant and stops for a 6-second barking hello-and-smell. Remembering some important business, Sirius breaks off the conversation at t = 10 s and sprints back to the hydrant, where he stays for 4 s and then leisurely pads back to his starting point. (b) Sirius is at rest during segments B (while chatting with Fido) and D (while at the hydrant). Notice that the graph is a horizontal line while Sirius is at rest. (c) Sirius is moving to the right whenever x is increasing. That is only during segment A. Don't confuse something going right on the graph (such as segments C and E) with the object physically moving to the right (as in segment A). Just because t is increasing doesn't mean x is. (d) The speed is the magnitude of the slope of the graph. Both segments C and E have negative slope, but C's slope is steeper, so Sirius has a greater speed during segment C than during segment E. Assess: We stated our assumption (that the origin is at the hydrant) explicitly. During segments B and D time continues to increase but the position remains constant; this corresponds to zero velocity.

In the previous problem, what is the velocity of the object from t=4s to t=7s?

0 m/s

A bucket has a volume of 1560 cm^3. What is its volume in m^3?

0.00156 or 1.56 * 10^-3

An insect crawls along the edge of a rectangular swimming pool of length 27 m and width 21 m. If it crawls from corner A to corner B in 30 min, What is its average velocity?

0.026 m/s

Given the displacement-time graph below, what is the velocity of the object during the first 4 seconds?

0.5 m/s

During a 50-min physics class, how far (in meters) will the ends of the hair on your head move? Assuming that the hair grows at an average rate of 1.5 cm per month on a human head hair.

1.) convert cm to m 2.) convert min to seconds = 1.7 x 10^-5 m

A stunt man drives a car off a 10.0-m-high cliff at a speed of 20 m/s. How far does the car land from the base of the cliff?

1.) solve for t first with Y=Yo + Vyo(t) - 1/2 (a)(t^2) t=1.43 seconds 2.) solve for X X = Xo + at X = 0 + (20)(1.43) X= 28.6 m

A runner runs 350 m due East, then turns around and runs 550 m due West. What is the total displacement of the runner relative to the starting position? Distance Traveled?

200 m due west or -200 m

4310 cm^3 = How many cubic meters?

4.31 ×10^-3 m^3

What are the x and y components of the vector that must be added to the following three vectors, so that the sum of the four vectors is zero? Due east is the +x direction and due north is the +y direction. A~ = 113 units, 60◦ south of west B~ = 222 units, 35◦ south of east C~ = 177 units, 23◦ north of east

Dx = 113 cos 60◦ − 222 cos 35◦ − 177 cos 23◦ = −288 units Dy = 113 sin 60◦ + 222 sin 35◦ − 177 sin 23◦ = 156 units

You can launch a projectile with a fixed initial speed but at any angle above the horizontal, and it feels no air resistance. The time for it to return to the ground does not depend on the angle at which you launch it.

False

The interior of a popular microwave oven has a width W = 15.5 in, a depth D = 14.5 in, and a height H = 9.25 in. What is the interior volume of the oven in SI units?

First, convert the width, depth, and height of the oven to meters: V = W × D × H = 0.394 m × 0.368 m × 0.23= 0.034 m^3

A force vector points at angle of 52◦ above the +x axis. It has a y component of +290 newtons. Find: (a) the magnitude of the force vector (b) the x component of the force vector

Fy= 290 N Fy=Fsin(theta) F= sin(theta)/Fy F= (sin(52))/(290) = 368 N Fx=Fcos(theta) Fx=368(cos(52)) Fx= 226.56 N

An airplane lands with an initial velocity of 70.0 m/s and then decelerates at 1.50 m/s2 for 40.0 s. What is its final velocity?

Given Initial velocity = 70 m/s Acceleration = -1.5 m/s² Time = 40 second According to equation of motion V = Vo + at V = 70 - (1.5 × 40) V = 70 - 60 V = 10 m/s So final velocity will be 10 m/s

A projectile is fired from the origin (at y = 0 m) as shown in the figure. The initial velocity components are v0x=940 m/s and v0y=96 m/s. The projectile reaches maximum height at point P, then it falls and strikes the ground at point Q. In the figure, the y-coordinate of point P is closest to:

Given The projectile is fired from origin. At x = 0 and y = 0 The initial velocity in x direction v0x = 940 m/s The initial velocity in y direction v0y = 96 m/s Solution When the projectile reaches point P, the velocity in y direction will be zero vPy^2 = voy^2 - 2gy 02 = 962 - 2 x 9.8 x y 19.6y = 962 y = 470.20 m So, the y coordinate of point P is closest to 470 m

A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal. It reaches its highest point and starts falling down. Which of the following statements about the rock's motion are true just before it hits the ground?

Its horizontal velocity component is the same as it was just as it was launched.

Suppose a golf ball is hit off the tee with an initial velocity of 30.0 m/s at an angle of 35° to the horizontal. (a) What is the maximum height reached by the ball? (b) What is its range?

Maximum height = (v^2 sin^2 (theta) ) / (2g) Range = (v^2 sin (2 theta)/ (g) v= velocity of projectile theta = angle of projectile g = acceleration due to gravity = 9.8 m/s2 a.) max height = 15.1 m b.) range = 86.3 m

The motion diagram shows a particle that is slowing down. The sign of the position x and the sign of the velocity vx are:

Position is positive, velocity is negative.

A football is kicked at an angle q with respect to the horizontal. Which one of the following statements best describes the acceleration of the football during this event if air resistance is neglected?

The acceleration is 9.8 m/s^2 at all times.

Suppose that a car traveling to the west begins to slow down as it approaches a traffic light. Which of the following statements about its acceleration is correct?

The acceleration is toward the east.

In two-dimensional motion in the x-y plane, what is the relationship between the x part of the motion to the y part of the motion?

The x part of the motion is independent of the y part of the motion.

A baseball is hit upward at an angle to the horizontal and travels along a parabolic arc before it strikes the ground. Which one of the following statements is necessarily TRUE?

The x-component of the velocity of the ball is the same throughout the ball's flight.

A projectile is fired from the origin (at y = 0 m) as shown in the figure. The initial velocity components are v0x=490 m/s and v0y=35 m/s. The projectile reaches maximum height at point P, then it falls and strikes the ground at point Q. In the figure, the y-component of the velocity of the shell of point P is closest to:

The y-component of projectile is zero at the top most point in trajectory.hence the answer is zero

Consider a deer that runs from point A to point B. The distance the deer runs can be greater than the magnitude of its displacement, but the magnitude of the displacement can never be greater than the distance it runs.

True

A cyclist is at rest at a traffic light. When the light turns green, he begins accelerating at 1.2 m/s2. How many seconds after the light turns green does he reach his cruising speed of 6.0 m/s?

V=Vo+at 6.0=0+(1.2 x t) t= 6/1.2 t= 5 seconds

A Saturn V rocket is launched straight up with a constant acceleration of 18 m/s2. After 150 s, how fast is the rocket moving and how far has it traveled?

V=Vo+at V=0+(18 x 150) V= 2700 m/s speed S= (Vo x t) - (0.5 x at^2) S=(0 x 150) - (0.5 x 18(150^2)) S= 202,500 m traveled

One second after being thrown straight down, an object is falling with a speed of 20 m/s. How fast will it be falling 2 seconds later?

V=Vo+at V=? Vo=20 m/s a= -9.8 m/s t= 2 seconds V=20 + (-9.8 x 2) V= 40 m/s

Trained dolphins are capable of a vertical leap of 7.0 m straight up from the surface of the water-an impressive feat. Suppose you could train a dolphin to launch itself out of the water at this same speed but at an angle. What maximum horizontal range could the dolphin achieve?

We know the angle should be 45* the maximum height equation is given as H = v2 sin2 / 2g 7 = v2 sin 90 / 2 * 9.8 v = sqrt ( 7 *2 * 9.8) v = 11.71 m/s Therefore, R = v^2 sin^2 / g R = 11.712 sin^2 *45 / 9.8 R = 14 m

If an object is thrown straight upward with an initial speed of 8 m/s and take 3 seconds to strike the ground, from what height was the object thrown?

X - Xo = Vo t + 0.5 at^2 Xo=? X=0 Vo= 8 m/s a= -9.8 m/s t= 3 0-Xo= 8(3) + (0.5(-9.8)(3^2)) X= 21 m

A young girl standing on a bridge throws a stone with an initial velocity of 12 m/s at a downward angle of 45° to the horizontal, in an attempt to hit a block of wood floating in the river below. If the stone is thrown from a height of the bridge, does the stone hit the block?

Y - Yo=Vyo(t) - 1/2 (a)(t^2) Voy= Vo(cos(theta)) Voy= 12 cos (45) = -8.49 ay= -9.8 m/s -20=(-8.49)(t)-1/2(-9.8)(t^2) t = 1.33 sec x=vt x= (-8.49)(1.33) x= 11.29 m so NO it is short

A rifle is aimed horizontally at a target 50 m away. The bullet hits the target 2.0 cm below the aim point. (a) What was the bullet's flight time? (b) What was the bullet's speed as it left the barrel?

a.) 0.064 sec b.) 780 m/s

A baseball player throws a ball at a 40◦ angle to the ground. The ball lands on the ground some distance away. Is there any point on the trajectory where ~v and ~a are parallel? Is there any point where ~v and ~a are perpendicular to each other? If so, where?

a.) the ball cannot move downward, so the velocity and acceleration cannot be parallel b.) at the point at maximum height the velocity and acceleration are perpendicular

The motion diagram shows a particle that is slowing down. The sign of the acceleration ax is:

a= V-Vo/t2-t1 velocity is negative and acceleration is positive (they are inverse)

Anna walks 90 m due east and then 50 m due north. What is her displacement from her starting point? How about the direction?

about 103 m Northeast

A ball tossed vertically upward rises, reaches its highest point, and then falls back to its starting point. During this time the acceleration of the ball is always

always due to gravity directed downward.

A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will

be directly over the package.

If an object moves with constant acceleration, its velocity must

change by the same amount each second.

The motion of a particle is described in the velocity vs. time graph shown in the figure. Over the nine-second interval shown, we can say that the speed of the particle

decreases and then increases.

An elevator is moving downward. It is slowing down as it approaches the ground floor. Adapt the information in the figure to determine which of the following velocity graphs best represents the motion of the elevator.

downward velocity with positive acceleration leads to a graph below the x axis with a positive slope

Which of the following graphs represent an object having zero acceleration?

graphs a and b because graph a has position vs time and it is constant

A 10-kg rock and a 20-kg rock are thrown upward with the same initial speed v0 and experience no significant air resistance. If the 10-kg rock reaches a maximum height h, what maximum height will the 20-kg ball reach?

h

In a soccer free kick, a player kicks a stationary ball toward the goal that is 18 m away. He kicks the ball at an angle of 22◦ from the horizontal at a speed of 23 m/s. (a) How long does the ball take to reach the goal? (b) How far off the ground is the ball when it reaches the goal?

height of soccer goal 8ft = 2.43 meter, range of the ball is 37.49 meter and maximum height is 3.78 meter so the it will not make a goal and the ball will go above the goal.

As you drive in your car at 15 m/s (just a bit under 35 mph), you see a child's ball roll into the street ahead of you. You hit the brakes and stop as quickly as you can. In this case, you come to rest in 1.5 s. How far does your car travel as you brake to a stop?

initial velocity is Vo = 15 m/sec final velocity is V = 0 m/sec time taken is t= 1.5 sec acceleration is a = (V-Vo)/t2-t1 = (0-15)/1.5 = -10 m/s^2 distance travelled is S = (Vo*t)-(0.5*a*t^2) S = (15*1.5)-(0.5*10*1.5^2) S = 11.25 m is the distance travelled before coming to rest after breaks applied

What is the maximum distance we can shoot a dart, provided our toy dart gun gives a maximum initial velocity of 7.76 m/s?

maximum Range= V^2/g = 6.14 m

A tennis player hits a ball 2.0 m above the ground. The ball leaves his racquet with a speed of 20 m/s at an angle of 5.0◦ above the horizontal. The horizontal distance to the net is 7.0 m, and the net is 1.0 m high. Does the ball clear the net? If so, by how much? If not, by how much does it miss?

t= 0.351 s The vertical position at t = 0.351 s = 2.0 m so the ball clears the net by 1.0 m

A particle moves with the velocity-versus-time graph shown here. At which labeled point is the magnitude of the acceleration the greatest?

the steeper the slope the higher the acceleration

Two chains of length 1.0 m are used to support a lamp, as shown. The distance between the two chains along the ceiling is 1.0 m. What is the vertical distance from the lamp to the ceiling?

using pytha goras theorem: we get : x^2 = (1^2 - 0.5^2) x = 0.866m

A projectile is fired from the origin (at y = 0 m) as shown in the figure. The initial velocity components are v0x=140 m/s and v0y=84 m/s. The projectile reaches maximum height at point P, then it falls and strikes the ground at point Q. In the figure, the x-component of the velocity of the shell at point P is closest to:

x-component of the velocity of the shell at point P = V0x = 140m/s