Chapter 2, Problem 14Q

To determine

To Explain: The way to estimate the maximum height to which one can throw a ball vertically upwards and the maximum speed that can be given to it.

Explanation of Solution

Introduction:

A projectile motion is referred to a type of motion that an object has when it is thrown with a force and which falls under the influence of gravity alone.

In order to estimate the maximum height, throw the ball vertically upwards and note the time in which it falls. Divide the time by 2 and use it in second equation of motion. At the maximum height, the instantaneous velocity is zero.

  $\begin{array}{l}y=ut+\frac{1}{2}a{t}^2\\ h_{\max }=0+\frac{1}{2}g{t}^2\end{array}$

Here, g is the acceleration due to gravity.

For the maximum speed which can be given, put the time in first equation of motion.

  $\begin{array}{l}v=u+at\\ 0=u-gt\\ u=gt\end{array}$

Here, v is the final velocity which is 0 at the maximum height and u is the initial velocity.