A ball is thrown vertically upward with a velocity u from the top of a tower. If it strikes the ground with velocity 3u, the time taken by the ball to reach the ground is?

Question

Answer

Time taken by ball to reach the ground when thrown vertically upward

Given data:

Initial velocity of ball, u

Velocity of ball when it strikes the ground, 3u

Solution:

Step 1: Finding the time taken for the ball to reach maximum height

When the ball is thrown vertically upward, the only force acting on it is the force of gravity.

Let's assume the initial height of the ball to be h.

The equation of motion for the ball when it is thrown vertically upward is given by:

v = u - gt

h = ut - (1/2)gt^2

Where, v is the final velocity of the ball, g is the acceleration due to gravity (-9.8 m/s^2), and t is the time taken by the ball to reach maximum height.

At the maximum height, the velocity of the ball becomes zero.

So, v = 0. Therefore, we can find the time taken by the ball to reach maximum height using the equation:

0 = u - gt

t = u/g

Step 2: Finding the time taken for the ball to fall back to its initial height

After reaching the maximum height, the ball falls back to its initial height.

The time taken for the ball to fall back to its initial height is the same as the time taken for the ball to reach the maximum height.

Therefore, the total time taken by the ball to go up and come back down to its initial height is:

T = 2t = 2u/g

Step 3: Finding the time taken for the ball to reach the ground

Now, we know that the ball strikes the ground with a velocity of 3u.

Let's assume the time taken by the ball to reach the ground from the maximum height is t'.

The equation of motion for the ball when it falls from the maximum height to the ground is given by:

v = 3u - gt'

h = (3u)t' - (1/2)gt'^2

Where, v is the final velocity of the ball, h is the height from which the ball is falling, and t' is the time taken by the ball to reach the ground from the maximum height.

At the ground level, the height of the ball becomes zero.

So, h = 0. Therefore,

Answer

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