Physics Test Review
Find the polar coordinates responding to (x, y) = (-3.25m, 1.50m).
(r, Θ) = (3.58m, 155˚)
(Find the Cartesian coordinates corresponding to (r, Θ) = (4.00m, 53.0˚).
(x, y) = (2.41m, 2.19m)
A firkin is an old British unit of volume equal to 9 gallons. How many cubic meters are there in 8.40 firkins?
.286 m^3
A study from the National Institutes of Health states that the human body contains trillions of microorganisms that make up 1 - 3% of the body's mass. Use this information to estimate the average mass of a microorganism.
1.10^-14 kg
The magnitudes of two vectors A and B are 12 units and 8 units, respectively. What are the largest and smallest possible values for the magnitude of the resultant vector R = A + B?
20 and 4
Convert 4.50 x 10^3 kg/m^3 to g/cm^3.
4.50 g/cm^3
If a car is traveling at a speed of 28.0 m/s, is the driver exceeding the speed limit of 55.0 mi/h?
62.6 mi/h, so yes.
Convert 152 mi/h to m/s.
67.9 m/s
The traffic light turns green, and the driver of a high-performance car slams the accelerator to the floor. The acceleromater registers 22.0 m/s^2. Convert this reading to km/min^2.
79.2 km/min^2
True or False: An equation that is dimensionally correct is always physically correct, up to a constant of proportionality.
False
True or False: Replacing v by r/t in the final answer also gives a dimensionally correct equation.
False
Determine whether the equation x = vt^2 is dimensionally correct. If not, provide a correct expression, up to an overall constant of proportionality.
It's incorrect. x = vt is correct.
The map below shows that Atlanta is 730 miles in a direction 5.00˚ north of east from Dallas, and that Chicago is 560 miles in a direction 21.0˚ west of north from Atlanta. Assuming the Earth may be approximated as flat across the map, what is the displacement from Dallas to Chicago? Find its magnitude (in mi) and direction (in degrees) as measured counterclockwise from due east of Dallas.
Magnitude = 788.08 miles Direction = 48.08 degrees
The left side of an equation has dimensions of length and the right side has dimensions of length squared. Can the equation be correct (choose one)?
No, because the equation is dimensionally inconsistent.
A 2.00m tall basketball player is standing on the floor 10.0m from the basket, as in the figure below. If he shoots the ball at a 40.0˚ angle with the horizontal, at which initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basketball is 3.05m.
V = 10.67 m/s (?)
A ball thrown straight up into the air is found to be moving at 7.99 m/s after falling 2.97m below its release point. Find the ball's initial speed (in m/s).
Vi = 2.37 m/s
One of the fastest recorded pitches in a major-league baseball, thrown by Tim Lincecum in 2009, was clocked at 101.0 mi/h. If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, 60.5 ft away?
Yf = 0.818
Find a relationship between an acceleration of constant magnitude a, speed v, and distance r from the origin for a particle traveling in a circle.
[a] = L/T^2 > [v] = L/T > T = L/[v] > [a] = L/T^2 = L/(L/[v])^2 = [v]^2/L >[a] = [v]^2/[r] > a = v^2/r
The graph (in homework) below shows position verses time for a basketball player moving along a straight-line path. What is the basketball players average velocity (in m/s) over the following time intervals? (Indicate the direction with the signs of your answers.) a) 0 to 1.00s b) 0 to 4.00s c) 1.00 to 5.00s d 0 to 5.00s
a) 12 m/s b) -1.5 m/s c) -3 m/s d) 0 m/s
A car accelerates uniformly from rest to a speed of 55.0 mi/h in 12.0 s. a) Find the distance the car travels during this time. b) Find the constant acceleration of the car.
a) 147.49 b) 2.048 m/s^2
A mountain climber stands at the top of a 35.5m cliff that overhangs a calm pool of water. She throws two stones vertically downward 1.00s apart and observes that they cause a single splash. The first stone had an initial velocity of -2.80 m/s. (Indicate the direction with the sign of your answers). a) How long after release of the first stone did the two stones hit the water? (Round your answer to at least two decimal places.) b) What initial velocity must the second stone have had, given that they hit he water simultaneously? c) What was the velocity of each stone at the instant it hit the water?
a) 2.42 s b) -18.04 m/s c) 26.0
A rectangle has a length of (2.7 ± 0.1)m and a width of (1.3 ± 0.1)m. Calculate the area and the perimeter of the rectangle, and give the uncertainty in each value. a) Calculate the area and give its uncertainty (in m^2) b) Calculate the perimeter of the rectangle and give its uncertainty (in m)
a) 3.5 ± .4 b) 8.0 ± .4
A person measures the height of a building by walking out a distance of 46.0m from its base and shining a flashlight beam towards the top. When the beam is elevated at an angle at 39.0˚ with respect to the horizontal, the beam strikes the top of the building. a) If the flashlight at a height of 2.00m, find the height of the building b) Calculate the length of the light beam
a) 39.3 m b) 59.2 m
A ranch has two fenced rectangular areas. Area A has a length of 750m and a width of 125m, and area B has length 400m and width 150m Find: a) area A b) area B c) the total area, with attention to the rules of significant figures. Assume trailing zeros are not significant.
a) 9.4 x 10^4 m^2 b) 6 x 10^4 m^2 c) 1.5 x 10^5 m^2
Two boats start together and race across a 52 km wide lake and back. Boat A goes across at 52 km/h and returns at 52 km/h. Boat B goes across at 26 km/h, and its crew, realizing how far behind it is getting, returns at 78 km/h. Turnaround times are negligible, and the boat that completes the round-trip first wins. a) Which boat wins? (Or is it a tie?) By how much? b) What is the average velocity of the winning boat?
a) Boat A; 52km b) 0 km/h
A certain free falling object, released from rest, requires 1.30s to travel the last 28.0m above the ground. a) Find the velocity of the object when it is 28.0m above the ground (Indicate the direction with the sign of your answer. Let the positive direction be upward.) b) Find the total distance the object travels during the fall.
a) Vf = -15.17 m/s b) d = 39.73
A student throws a pair of keys vertically upward to his fraternity brother, who is in a window 4.15m above. The brother's outstretched hand catches t keys 1.75s later. (Take upward as the positive direction. Indicate the direction with the sign of your answer.) a) With what initial velocity were the keys thrown? b) What was the velocity of the keys just before they were caught?
a) Vi = 10.95 m/s b) Vf = -6.2 m/s
A boy throws a baseball onto a roof and rolls back down and off the roof with a speed to 4.30 m/s. If the roof is pitched at 38.0˚ below the horizon and the roof edge is 3.30m above the ground, find the time the baseball spends in the air and the horizontal distance from the roof edge to the point where the baseball lands on the ground. a) The time the baseball spends in the air (in s) b) The horizontal distance from the roof edge to the point where the baseball lands on the ground
a) t = .594 s b) ΔX = 2.01
An airplane maintains a speed of 621 km/h relative to the air it is flying through as it makes a trip to a city 752 km away to the North. (Assume North is the positive y-direction and east is the positive x-direction.) a) What time interval is required for the trip if the plane flies through a headwind blowing at 36.9 km/h toward the south? b) What time interval is required if there is a tailwind with the same speed? c) What time interval is required if there is a crosswind blowing at 36.9 km/h to the east relative the ground?
a) t = 1.29 h b) t = 1.14 h c) 1.21 h
In a scene from a television show, a car rolls down an incline and off a vertical cliff, falling into the river below. The car starts from rest and rolls down the incline, which makes an angle of 25.0˚ below the horizontal, with a constant acceleration of 3.97 m/s^2. After rolling down the incline a distance of 55.0m, it reaches the edge of a cliff, which is 35.0m above the river. a) How much time (in s) does it take the car to fall from the edge of the cliff to the landing point? b) At the point where the car lands in the river, how far is it horizontally from the edge of the cliff (in m)?
a) t = 1.94 b) ΔX = 36.74
A tortoise can run with a speed of 0.12 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 1.0 minutes. The tortoise wins by a shell (30cm). a) How long does the race take? b) What is the length of the race?
a) t = 63.03s b) d = 7.56m
A miniature quadcopter is located at xi = 1.75 m and yi = -3.70 m at t = 0 and moves with an average velocity having components vav, x = 2.20 m/s and vav, y = -2.50 m/s. What are the x-coordinate and y-coordinate (in m) of the quadcopter's position at t = 3.10s
a) x-coordinate Figure this one out?
A hiker walks 2.80 km south and then 2.75 km east, all in 2.00 hours. a) Calculate the magnitude (in km) and direction (in degrees of south of east) of the hiker's displacement during the given time. b) Calculate the magnitude (in km/h) and direction (in degrees south of east) of the hiker's average velocity during the given time. c) What was her average speed (in km/h) during the same time interval?
a) Θ = 45.5˚ b) Magnitude = 1.965 km/h; Direction does not change c) 2.78 km/h
Two points are given in polar coordinates by (r, Θ) = (2.20 m, 50.0˚) and (r, Θ) = (3.60 m, -56.0˚), respectively . What is the distance between them?
d = 4.7
Newton's law of universal gravitation can be expressed by the equation F = G(Mm/r^2) where F is the gravitational force, M and m are masses, are r is a length. Force has the SI units kg * m/s^2. What are the SI units of the proportionality constant G?
m^3/kg*s^2
Nerve impulses in a human body travel at a speed of about 100 m/s. Suppose a man accidentally stubs his toe. About how much time does it take the nerve impulses to travel the foot to the brain (in s)? Assume the man is 1.90m tall and the nerve impulse travels at uniform speed.
t = .019 sec
The average person passes out at an acceleration of 7g (that is, seven times the gravitational acceleration on Earth). Suppose a car is designed to accelerate at this rate. How much time would be required for the car to accelerate from rest to 70.3 miles per hour? (The car would need rocket boosters!) Gravitational Acceleration of Earth - 32.2 ft/s^2
t = .4574
A ladder 6.60m long leans against the side of a building . If the ladder is inclined at an angle of 65.0˚ to the horizontal, what is the horizontal distance from the bottom of the ladder of the building?
x = 2.79m
A point is located in a polar coordinate system by the coordinates r = 7.0m and Θ = 20˚. Find the x- and y- coordinates of this point, assuming that the two coordinate systems have the same origin.
x = 6.58 y = 2.394
A train is traveling down a straight track at 22 m/s when the engineer applies the breaks, resulting in an acceleration of -1.0 m/s^2 as long as the train is in motion. How far does the train move during a 44s time interval starting at the instant the breaks are applied?
Δx = 242m
