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Chapter 7: 84GP (page 170)

A golf ball rolls off the top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.00 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

Short Answer

Expert verified

The golf ball rises to the same height of 4 m after every bounce.

Step by step solution

01

Identification of the given data

The vertical height of the total no. of steps is\(h = 4\;{\rm{m}}\).

The width of each step is\(d = 1\;{\rm{m}}\).

02

Meaning of a perfectly elastic collision

In a perfectly elastic collision, the linear momentum of the system and its total energy remains conserved.

03

Analysis of the motion of the golf ball

Here, the golf ball bounces back from every step with no loss in energy. The coefficient of restitution is given as:

\(e = \frac{{{\rm{Relative}}\;{\rm{velocity}}\;{\rm{of}}\;{\rm{separation}}}}{{{\rm{Relative}}\;{\rm{velocity}}\;{\rm{of}}\;{\rm{approach}}}}\)

For a perfectly elastic collision,\(e = 1\)such that

\(\begin{aligned}{c}1 = \frac{{{v_{\rm{f}}}}}{{{v_{\rm{i}}}}}\\{v_{\rm{f}}} = {v_{\rm{i}}}\end{aligned}\)

This implies that the golf ball bounces at the same speed. Therefore, it rises to the same height after every bounce, i.e., 4 m.

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Most popular questions from this chapter

An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90掳.

(a) At what angle does the target particle move after the collision?

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Car A hits car B (initially at rest and of equal mass) from behind while going\(38\;{\rm{m/s}}\). Immediately after the collision, car B moves forward at\(15\;{\rm{m/s}}\)and car A is at rest. What fraction of the initial kinetic energy is lost in the collision?

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A 0.25-kg skeet (clay target) is fired at an angle of 28掳 to the horizontal with a speed of\(25\;{\rm{m/s}}\)(Fig. 7鈥�45). When it reaches the maximum height, h, it is hit from below by a 15-g pellet traveling vertically upward at a speed of\(230\;{\rm{m/s}}\).The pellet is embedded in the skeet. (a) How much higher,\(h'\)does the skeet go up? (b) How much extra distance, does the skeet travel because of the collision?

Billiard ball A of mass \({m_{\rm{A}}} = 0.120\;{\rm{kg}}\) moving with speed \({v_{\rm{A}}} = 2.80\;{\rm{m/s}}\) strikes ball B, initially at rest, of mass \({m_{\rm{B}}} = 0.140\;{\rm{kg}}\) As a result of the collision, ball A is deflected off at an angle of 30.0掳 with a speed \({v'_{\rm{A}}} = 2.10\;{\rm{m/s}}\)

(a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately.

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