Problem Statement: A ball is projected from the ground with 50m/s. At the maximum height, velocity is 30m/s. Calculate the time after which it will reach the ground again.

Solution:

To solve this problem, we can use the concept of projectile motion. The motion of the ball can be divided into two parts: the upward motion and the downward motion.

Step 1: Find the time taken by the ball to reach maximum height.

The initial velocity of the ball is 50m/s and the final velocity at maximum height is 30m/s. The acceleration due to gravity is -9.8m/s^2 (negative as it acts in the opposite direction to the motion of the ball).

Using the equation of motion, v = u + at, we can find the time taken by the ball to reach the maximum height.

30 = 50 - 9.8t
t = 2.04 seconds

Therefore, the time taken by the ball to reach the maximum height is 2.04 seconds.

Step 2: Find the total time taken by the ball to reach the ground.

The time taken by the ball to reach the maximum height is equal to the time taken by the ball to reach half of its total journey (upward motion).

Therefore, the total time taken by the ball to reach the ground again is twice the time taken by the ball to reach the maximum height.

Total time taken = 2 x 2.04 = 4.08 seconds

Therefore, the ball will reach the ground again after 4.08 seconds.

Conclusion: The ball will reach the ground again after 4.08 seconds.