Question

A ball is thrown vertically downward with a velocity of 20m/s from the top of a tower. It hits the ground after some time with a velocity of 80m/s. The height of the tower is : (g = $10m/s^2$)

• A. 360 m
• B. 340 m
• C. 320 m
• D. 300 m

Answer 1

The Correct Option is D

To determine the height of the tower from which the ball is thrown, we can use the equations of motion. Here, we are given:

• Initial velocity, \(u = 20 \, \text{m/s}\)
• Final velocity, \(v = 80 \, \text{m/s}\)
• Acceleration due to gravity, \(g = 10 \, \text{m/s}^2\)

We need to find the height of the tower, \(h\). We can use the following equation of motion:

\(v^2 = u^2 + 2gh\)

Substitute the known values into the equation:

\(80^2 = 20^2 + 2 \cdot 10 \cdot h\)

Calculate the squares:

\(6400 = 400 + 20h\)

Rearrange to solve for \(h\):

\(6400 - 400 = 20h\)

\(6000 = 20h\)

Divide both sides by 20:

\(h = \frac{6000}{20} = 300 \, \text{m}\)

Thus, the height of the tower is 300 meters.

Therefore, the correct answer is: 300 m.