Chapter 14, Problem 1A

If we drop a ball from rest, how far will it fall vertically in the first second? If we instead move our hand horizontally and drop it (throw it), how far will it fall vertically in the first second?

To determine

To Calculate: The distance through which the ball drops when released from rest in the first second if dropped vertically and if thrown horizontally.

Explanation of Solution

Given:

Initial velocity of the ball, $u=0$

Time interval, $t=1\text{s}$

Acceleration due to gravity, $a=g=9.8{\text{m/s}}^{\text{2}}$

Formula Used:

Second equation of motion: $s=ut+\frac{1}{2}a{t}^2$

Here, s is the displacement, u is the initial velocity, a is the acceleration and t is the time.

Calculations:

In both the case, the vertical motion is governed by gravity only. Thus, the vertical displacement for both cases would be as follows:

$\begin{array}{l}s=ut+\frac{1}{2}a{t}^2\\ s=0+\frac{1}{2}\left(9.8\right){\left(1\right)}^2\\ s=4.9\text{m}\end{array}$

None of the factors is affected by the way the ball is thrown.

Conclusion:

Thus, the distance through which the ball drops when released from rest in the first second is $4.9\text{m}$ .