Chapter 5, Problem 105A

(a)

To determine

The appropriate analysis TO-DETERMINE who is correct.

Answer to Problem 105A

From the appropriate analysis the K is correct.

Explanation of Solution

Given:

For anybody sliding down on an inclined plane the acceleration is

  $a=g\sin \theta$

And, the body is slides from rest, so the initial velocity $u=0$

Formula used:

From the equation of motion

  $\begin{array}{l}v=u+at\\ v=0+at\\ v=at\\ \text{t=}\frac{v}{a}\mathrm{......}\left(1\right)\end{array}$

Calculation:

From equation of motion

  $\begin{array}{l}{v}^2=u^2+2as\\ v^2=2as\\ v=\sqrt{2as}\\ v^2=u^2+2as\\ v^2=2as\\ v=\sqrt{2\left(g\sin \theta \right)s}\\ v=\sqrt{2sg\sin \theta }\end{array}$

Now from equation (1)

  $\begin{array}{l}t=\frac{\sqrt{2sg\sin \theta }}{g\sin \theta }\\ t=\sqrt{\frac{2s}{g\sin \theta }}\end{array}$

Conclusion:

This means the time of sliding down on an inclined plane does not depend on the mass of the body which slides.

So, the K is correct.

(b)

To determine

To calculate:How many seconds of difference there will be between the two times.

Answer to Problem 105A

There is no difference between their times of sliding.

Explanation of Solution

Since, the time taken to slide on an inclined plane for both man and the boy is same. So, there is no difference between their times of sliding.

Conclusion:

There is no difference between their times of sliding.