A ball rolls off a platform that is 5 meters above the ground. The ball's horizontal velocity as it leaves the platform is 4.8 m/s.
(a) How much time does it take for the ball to hit the ground? (Use g = 10 m/s2.)
. s
To find the time it takes for the ball to hit the ground, we can use the equation of motion for vertical motion:
s = ut + (1/2)gt^2
Where:
s = vertical distance traveled (in this case, 5 meters)
u = initial vertical velocity (in this case, 0 m/s, as the ball starts from rest on the platform)
t = time taken
g = acceleration due to gravity (in this case, 10 m/s^2)
Since the initial vertical velocity is 0 m/s and the ball falls vertically downwards, we can simplify the equation to:
s = (1/2)gt^2
Plugging in the values, we get:
5 = (1/2)(10)(t^2)
Simplifying further:
5 = 5t^2
Dividing both sides by 5:
1 = t^2
Taking the square root of both sides:
t = 1 second
Therefore, it takes 1 second for the ball to hit the ground.