A boy standing at the top of a tower of $20\,m$ height drops a stone. Assuming $g = 10\, ms^{-2},$ the velocity with which it hits the ground is

Question

A car starts from rest and accelerates uniformly at 3 m/s\textsuperscript{2. What will be its velocity after 5 seconds?}

Answer 1

To determine the velocity with which the stone hits the ground, we use the equations of motion under the influence of gravity. Here, the stone is dropped from a height, meaning its initial velocity u = 0. Given, the height of the tower is h = 20\,m and acceleration due to gravity g = 10\,ms^{-2}. We need to find the final velocity v of the stone when it hits the ground.

We use the following equation of motion:

v^2 = u^2 + 2gh

Since the initial velocity u = 0, the equation simplifies to:

v^2 = 2gh

Substituting the known values:

v^2 = 2 \times 10 \, \text{m/s}^2 \times 20 \, \text{m} = 400 \, \text{m}^2/\text{s}^2

Taking the square root on both sides to find v:

v = \sqrt{400} = 20 \, \text{m/s}

Therefore, the velocity with which the stone hits the ground is 20.0 \, m/s.

Thus, the correct answer is 20.0\, m/s. Other options do not satisfy the result calculated from the formula, and hence are incorrect.

Answer 2