2. 1D Motion / Kinematics

A rock is thrown vertically upward with a speed of 27.0 m/s from the roof of a 31.0-m-tall building. The rock doesn't hit the building on its way back down and lands in the street below. (a) What is the speed of the rock just before it hits the street? (b) How much time elapses from when the rock is thrown until it hits the street?

A student throws a set of keys vertically upward to her sorority sister who is in a window 14.00 m above. The second student catches the keys 1.50 s later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

(I) A stone is dropped from the top of a cliff. It is seen to hit the ground below after 3.25 s. How high is the cliff?

(I) If a car rolls gently (v₀ = 0) off a vertical cliff, how long does it take it to reach 55 km/h?

(II) Figure 2–42 shows the velocity of a train as a function of time.

(c) During what periods, if any, was the acceleration constant?

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(II) A baseball is hit almost straight up into the air with a speed of 22 m/s. Estimate

(a) how high it goes, and

(II) The best rebounders in basketball have a vertical leap (that is, the vertical movement of a fixed point on their body) of about 120 cm.

(b) How long are they in the air?

(II) A baseball is seen to pass upward by a window with a vertical speed of 13 m/s. If the ball was thrown by a person 18 m below on the street,

(c) when was it thrown, and

(II) Roger sees water balloons fall past his window. He notices that each balloon strikes the sidewalk 0.83 s after passing his window, 15 m above the sidewalk.

(b) Assuming the balloons are being released from rest, from what height are they being released?

(II) Pelicans tuck their wings and free-fall straight down when diving for fish. Suppose a pelican starts its dive from a height of 16.0 m and cannot change its path once committed. If it takes a fish 0.20 s to perform evasive action, at what minimum height must it spot the pelican to escape? Assume the fish is at the surface of the water.

(III) A falling stone takes 0.28 s to travel past a window 2.2 m tall (Fig. 2–49). From what height above the top of the window did the stone fall?

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(III) A toy rocket moving vertically upward passes by a 2.0-m-high window whose base is 8.0 m above the ground. The rocket takes 0.15 s to travel the 2.0 m height of the window. What was the launch speed of the rocket, and how high will it go? Assume the propellant is burned very quickly at blastoff.

A person jumps out a fourth-story window 18.0 m above a firefighter's safety net. The survivor stretches the net 1.0 m before coming to rest, Fig. 2–50. (a) What was the average deceleration experienced by the survivor when she was slowed to rest by the net? (b) What would you do to make it 'safer' (that is, to generate a smaller deceleration): would you stiffen or loosen the net? Explain. <IMAGE>

Suppose a car manufacturer tested its cars for front-end collisions by hauling them up on a crane and dropping them from a certain height. What height corresponds to a collision at

(b) 35 km/h?

(II) A rocket rises vertically, from rest, with an acceleration of 3.2 m/s² until it runs out of fuel at an altitude of 725 m. After this point, its acceleration is that of gravity, downward.

(c) What maximum altitude does the rocket reach?

(II) A helicopter is ascending vertically with a constant speed of 6.40 m/s. At a height of 105 m above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground? [Hint: What is v₀ for the package?]

Suppose a 65-kg person jumps from a height of 3.0 m down to the ground.

What is the speed of the person just before landing (Chapter 2)?

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Two children are playing on two trampolines. The first child bounces up one-and-a-half times higher than the second child. The initial speed upwards of the second child is 4.0 m/s.

(b) What is the initial speed of the first child?

A parachutist bails out of an airplane, and freely falls 75 m (ignore air friction). Then the parachute opens, and her acceleration is ― 1.5 m/s² (up). The parachutist reaches the ground with a speed of 1.5 m/s.

(a) From how high did she bail out of the plane?

Bill can throw a ball vertically at a speed 1.5 times faster than Joe can. How many times higher will Bill's ball go than Joe's?

(II) For an object falling freely from rest, show that the distance traveled during each successive second increases in the ratio of successive odd integers (1, 3, 5, etc.). (This was first shown by Galileo.) See Figs. 2–27 and 2–30.

(II) For an object falling freely from rest, show that the distance traveled during each successive second increases in the ratio of successive odd integers (1, 3, 5, etc.). (This was first shown by Galileo.) See Figs. 2–27 and 2–30.