Answered: A ball is thrown upward from roof top,…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A ball is thrown upward from roof top, 90 m above the ground. The ball rises, then falls and hits the ground. Ignore air resistance.

a) What is the initial velocity of the ball, if it takes the ball 9.4 s to hit the ground?

b) What is the maximum height reached by the ball?

Expert Solution

Step 1

Given data

The height of the rooftop is given as h = 90 m.
The time taken by the ball to reach the ground is t = 9.4 s.

Sign convention

Taking values in the upward direction as positive and negative in a downward direction.

a) The initial velocity of the ball is calculated by the second equation of motion as,

$s = u t + \frac{1}{2} a t^{2}$

Here, u is the initial velocity of the ball, a is the acceleration of the body in a downward direction which is gravitational acceleration and s is the displacement travelled by the ball which is equal to the height of the roof.

On putting the values as,

$\begin{array}{rcl} s & = & u t + \frac{1}{2} a t^{2} \\ - 90 m & = & u \times (9.4 s) + \frac{1}{2} \times (- 9.8 m / s^{2}) \times {(9.4 s)}^{2} \\ u \times (9.4 s) & = & - 90 m + 432.964 m \\ u & = & 36.485 m / s \end{array}$

Thus, the initial velocity of the ball is 36.485 m/s.

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