A ball is thrown vertically upwards from the ground with an initial velocity of 50ms-1. What is the total time spent by the ball in the air? (g = 10ms-2)

A ball is thrown vertically upwards from the ground with an initial velocity of 50ms^-1. What is the total time spent by the ball in the air? (g = 10ms^-2)

Answer Details

The total time spent by the ball in the air can be calculated using the kinematic equation: h = ut + 0.5gt^2 where h is the maximum height reached by the ball, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken for the ball to reach the maximum height and fall back to the ground. When the ball reaches its maximum height, its vertical velocity becomes zero. We can use this fact to find the maximum height reached by the ball: v = u + gt 0 = 50 - 10t t = 5 seconds u = 50 m/s h = ut + 0.5gt^2 h = (50 m/s)(5 s) + 0.5(10 m/s^2)(5 s)^2 h = 125 meters The time taken for the ball to reach the maximum height and fall back to the ground is twice the time taken for the ball to reach the maximum height: total time = 2t = 2 x 5s = 10s Therefore, the total time spent by the ball in the air is 10 seconds. Hence, the correct option is (C) 10.0s.