4 physics

A free-body diagram shows the forces acting upon an object. How is that object represented in the diagram?

a single point

A window washer is descending from the top of a skyscraper at a constant velocity of 0.5 m/s. He realizes he forgot his keys and asks his friend to drop them from the roof. He catches them at time t. Which of the following graphs shows the position of the keys as a function of time?

decrease exponentially until it gets to a certain t then decrease in a linear line

How many km/h are equal to 1.0m/s? Hint: Carry out the explicit steps involved in the conversion.

1 m/s is equal to 3.6 km/h. It is because 1 km = 1000 m and 1 hour = 3600 seconds.

Horizontal and vertical motions of a projectile are independent of each other. What is meant by this?

Any object in projectile motion falls at the same rate as an object in freefall, regardless of its horizontal velocity.

Which forces affect the motion of a system?

External forces

What is mass? What does it depend on?

Mass is the quantity of matter contained in an object and depends on the number and types of atoms in the object.

Anne drops a ball from the top of a building. John throws his ball down. Which ball has the greater acceleration just after release? Assume air resistance is negligible.

Neither - they both have the same acceleration

Two people are pushing a box with forces of equal strength: one to the west and one to the north. In what direction must you apply force to prevent the box from moving?

Southeast

A soccer ball is kicked with an initial speed and at an angle 𝜃θ. Which of the following statements is true?

The initial horizontal component of the velocity is equal to the final horizontal component of the velocity.

A water balloon cannon is fired at 30m/s at an angle of 50∘above the horizontal. How far away will it fall?

The range of the projectile is given by R=𝑣0^2sin2𝜃0/𝑔 R=(30m/s^2 x sin 2 x 50) / 9.8m/s^2 = 90.44m

A person attempts to cross a river in a straight line by navigating a boat at 15m/s. If the river flows at 5.0m/s from his left to right, what would be the magnitude of the boat's resultant velocity? In what direction would the boat go, relative to the straight line across it?

The resultant velocity of the boat will be 15.8m/s. The boat will go toward his right at an angle of 18.4∘ to a line drawn across the river. Vbg = sqrt (5^2 + 15^2) = 15.81 m/sec Direction = arctan (15/5) = 71.56 deg 90-71.56=18.4

Assume the ground is uniformly level. If the horizontal component a projectile's velocity is doubled, but the vertical component is unchanged, what is the effect on the time of flight?

The time to reach the ground would remain the same since the vertical component is unchanged.

Two objects, with the same size and weight, are thrown from the top of a building at the same time. Standing on the edge of the roof, the first is thrown straight down the side of the building with an initial velocity of 2.5m/s while the second is thrown at 5.0m/s at an angle 30∘ below horizontal. Which will hit the ground first if the building is 60m high?

The two objects will hit at the same time.

A car travels at 60km/h60km/h. In 30s, it slows down to 20km/h. True or false: The car accelerated during this period.

True; Acceleration is a change in velocity divided by the time over which the change occurs. Velocity changes in this example, so an acceleration occurs. Note that acceleration can be negative.

Before we understood that objects have a tendency to maintain their velocity in a straight line unless acted upon by a net force, people thought that objects have a tendency to stop on their own. This happened because a specific force was not yet understood. What was that force?

frictional force

In the equation h=v0⁢y^2/2⁢g for the maximum height of a projectile, what does 𝑣0𝑦 stand for?

initial velocity in the y direction

Which of the following expressions shows the x-component of R→=A→+B→R→=A→+B→?

rx=ax+bx

Consider the following velocity vectors: Vector A: 3.4 m/s at 90° Vector B: 5.1 m/s at 180° What is the magnitude of the sum of these vectors?

sqrt A^2+B^2 sqrt (3.4)^2 + (5.1)^2 =6.129 m/s

Given the velocity of the river is 1.2m/s to the right and the velocity of the boat is 0.75 m/s straight

vtot = sqrt vx^2+vy^2 𝑣𝑥=𝑣river=1.20 m/s 𝑣𝑦=𝑣boat=0.750 m/s vtot = sqrt (1.20m/s)^2 + (0.750 m/s)^2 = 1.42 m/s 𝜃=tan^−1(𝑣𝑦/𝑣𝑥)=tan^−1(0.750/1.20)=32 degrees

Using the conventional choice for positive and negative axes described in the text, what is the y-component of the acceleration of an object experiencing projectile motion?

−9.8m/s^2

Calculate the wind velocity. The plane is known to be moving at 45.0 m/s due north relative to the air mass, while its velocity relative to the ground (its total velocity) is 38.0 m/s in a direction 20.0º west of north.

𝑣w𝑥=𝑣tot𝑥=𝑣totcos 110º 𝑣w𝑥=(38.0 m/s)(-0.342)=-13 m/s 𝑣w𝑦=(38.0 m/s)(0.940)−45.0 m/s=−9.29 m/s uw= sqrt vwx^2 + vwy^2 = sqrt (-13 m/s)^2 + (-9.29 m/s)^2 = 16 m/s 𝜃=tan^−1(𝑣w𝑦/𝑣w𝑥)=tan^−1(−9.29/−13.0)=35.6 degrees

During a fireworks display, a shell is shot into the air with an initial speed of 70.0 m/s at an angle of 75.0º above the horizontal. The fuse is timed to ignite the shell just as it reaches its highest point above the ground. (a) Calculate the height at which the shell explodes. (b) How much time passed between the launch of the shell and the explosion? (c) What is the horizontal displacement of the shell when it explodes?

𝑣𝑦^2=𝑣0y^2−2𝑔(𝑦−𝑦0) 0=𝑣0𝑦^2−2𝑔𝑦 𝑦=𝑣0𝑦^2/2𝑔 𝑣0𝑦=𝑣0sin𝜃0=(70.0 m/s)(sin 75º)=67.6 m/s. 𝑦=(67.6 m/s)^2/2(9.80 m/s^2) 𝑦=233m (a) 𝑦=1/2(𝑣0𝑦+𝑣𝑦)𝑡 𝑡=2𝑦/(𝑣0y+𝑣𝑦)=(2(33 m)(67.6 m/s))=6.90 s (b) 𝑥=𝑣𝑥𝑡 𝑣𝑥=𝑣0cos𝜃0=(70.0 m/s)(cos 75.0º)=18.1 m/s 𝑥=(18.1 m/s)(6.90 s)=125 m (c)

An airline passenger drops a coin while the plane is moving at 260 m/s. What is the velocity of the coin when it strikes the floor 1.50 m below its point of release: (a) Measured relative to the plane? (b) Measured relative to the Earth?

𝑣𝑦^2=𝑣0𝑦^2−2𝑔(𝑦−𝑦0) 𝑣𝑦^2=0^2−2(9.80m/s^2)(−1.50m−0 m)=29.4m^2/s^2 𝑣𝑦=−5.42 m/s (a) v= sqrt vx^2 + vy^2 v=sqrt (260m/s)^2 + (-5.42 m/s)^2 𝑣=260.06 m/s 𝜃=tan^−1(𝑣𝑦/𝑣𝑥)=tan−1(−5.42/260) 𝜃=tan−1(−0.0208)=−1.19º

Kilauea in Hawaii is the world's most continuously active volcano. Very active volcanoes characteristically eject red-hot rocks and lava rather than smoke and ash. Suppose a large rock is ejected from the volcano with a speed of 25.0 m/s and at an angle 35.0º above the horizontal. The rock strikes the side of the volcano at an altitude 20.0 m lower than its starting point. (a) Calculate the time it takes the rock to follow this path. (b) What are the magnitude and direction of the rock's velocity at impact?

𝑦=𝑦0+𝑣0𝑦𝑡−1/2𝑔𝑡^2 −20.0 m=(14.3 m/s)𝑡−(4.90 m/s^2)𝑡^2 (4.90 m/s^2)𝑡^2−(14.3 m/s)𝑡−(20.0 m)=0 use quadratic formula to find t where are 𝑎=4.90, 𝑏=-14.3, and 𝑐=-20.0 𝑡=3.96 s. (a) 𝑣𝑥=𝑣0cos𝜃0=(25.0 m/s)(cos 35º)=20.5 m/s 𝑣𝑦=𝑣0𝑦−𝑔𝑡 𝑣𝑦=14.3 m/s−(9.80 m/s^2)(3.96 s) 𝑣𝑦=−24.5 m/s v=sqrt vx^2 + vy^2 = sqrt (20.5m/s)^2 + (-24.5 m/s)^2=31.9 m/s 𝜃𝑣=tan^−1(𝑣𝑦/𝑣𝑥) 𝜃𝑣=tan^−1(−24.5/20.5)=tan^−1(−1.19)=−50.1º (b)

What is the direction of a vector whose x and y-components are both −5, with the angle measured from the positive x-axis?

𝜃=225∘