Chapter 6, Problem 72A

a.

To determine

Effect on time taken by rock to hit the ground.

Answer to Problem 72A

Time does not change.

Explanation of Solution

Given:

First throw: Rock is thrown horizontally.

Second throw: Rock is thrown horizontally even harder.

Ignore air resistance.

Formula Used:

From the equation of motion,

  $v=u+at$

Where, $u$ is initial velocity, $v$ is final velocity, $a$ is acceleration and $t$ is time.

Calculation:

Under gravity, $v=u-gt$

Since, rock is thrown horizontally, therefore the initial vertical velocity component is zero i.e. $u=0$

So,

  $\begin{array}{l}v=-gt\\ \Rightarrow t=-\frac{v}{g}\end{array}$

Hence, from the above equation it is clear that time taken to hit the ground depends only on vertical velocity and acceleration due to gravity.

So, in both case the ball hit the ground at same time.

Conclusion:

Time does not change.

b.

To determine

Effect on horizontal distance.

Answer to Problem 72A

The rock will cover longer horizontal distance in second throw.

Explanation of Solution

Given:

First throw: Rock is thrown horizontally.

Second throw: Rock is thrown horizontally even harder.

Ignore air resistance

Formula Used:

From the equation of motion,

  $s=ut+\frac{1}{2}a{t}^2$

Where, $u$ is initial velocity, $s$ is displacement, $a$ is acceleration and $t$ is time.

Calculation:

Since the rock is thrown harder in second throw. So, the initial horizontal speed will be higher.

From the equation it is clear that horizontal displacement is directly proportional to $u$ .

So, the rock will cover longer horizontal distance.

Conclusion:

The rock will cover longer horizontal distance in second throw due to higher initial speed $u$ .