A ball is projected horizontally from the top of a vertical cliff 40m high at a volocity of 20ms calculate the time taken ,the vertical component of velocity on getting to the ground
First, calculate the time taken for the ball to reach the ground.
The vertical motion equation for an object in free fall is:
h = (1/2)gt^2
where
h = height of the cliff = 40m
g = acceleration due to gravity = 9.81 m/s^2
t = time taken
Substitute the known values:
40 = (1/2)(9.81)(t)^2
80 = 9.81(t)^2
t^2 = 80/9.81
t ≈ √(80/9.81)
t ≈ √8.16
t ≈ 2.86 seconds
Now, calculate the vertical component of velocity when the ball reaches the ground.
The vertical velocity of an object in free fall can be calculated using the equation:
v = gt
where
v = vertical velocity
g = acceleration due to gravity = 9.81 m/s^2
t = time taken = 2.86 seconds
Substitute the values:
v = 9.81 * 2.86
v ≈ 28.05 m/s
Therefore, the time taken for the ball to reach the ground is approximately 2.86 seconds and the vertical component of velocity when it reaches the ground is approximately 28.05 m/s.