Question

A stone is thrown upwards with a velocity of 20 m/s from the roof of a building of height 10 m. At what velocity in m/s will it reach the ground assuming 10 m/s\(^2\) as acceleration due to gravity?

• A. \( \sqrt{200} \)
• B. \( \sqrt{300} \)
• C. \( \sqrt{500} \)
• D. \( \sqrt{600} \)

Hint:

For an object thrown upwards from a height, use the equation \( v^2 = u^2 + 2gh \) to find the final velocity, considering both initial velocity and the height of the fall.

Answer 1

The Correct Option is C

Step 1: Use the equation of motion for the final velocity.
The final velocity \( v \) of the stone can be calculated using the equation: \[ v^2 = u^2 + 2gh, \] where \( u = 20 \, \text{m/s} \) is the initial velocity, \( g = 10 \, \text{m/s}^2 \) is the acceleration due to gravity, and \( h = 10 \, \text{m} \) is the height of the building.
Step 2: Calculate the final velocity.
Substitute the values: \[ v^2 = 20^2 + 2 \times 10 \times 10 = 400 + 200 = 600, \] \[ v = \sqrt{600}. \]
Step 3: Conclusion.
Thus, the velocity with which the stone will reach the ground is \( \sqrt{600} \), which corresponds to option (D).