Chapter 2, Problem 33P

To determine

The height of the cliff

Answer to Problem 33P

51.75 m.

Explanation of Solution

Given:

Initial velocity of the stone $=v_i=0\frac{\text{m}}{\text{s}}$

Height of the cliff $=h$

Initial position of the stone at the top of the cliff $=y_i=h$

Final position of the stone at the ground $=y_f=0\text{m}$

Acceleration experienced by the stone during free fall $=a=g=9.8\frac{\text{m}}{{\text{s}}^{\text{2}}}$

Time taken by the stone to reach the ground $=t=32.5\sec$

Formula Used:

Position of an object at any during constant accelerated motion is given as

  $y_f=y_i+v_{i}t+(0.5)a{t}^2$

Calculation:

Consider that the motion of the stone is free fall.

Position of the stone at any time is given as

  $y_f=y_i+v_{i}t+(0.5)a{t}^2$

Substituting the values

  $\begin{array}{l}0=h+(0)(3.25)+(0.5)(-9.8){(}^{3.25}\\ h=51.75\text{m}\end{array}$

Conclusion:

Therefore, height of the cliff is 51.75 m.