A stone is thrown downward with an initial speed of 8m/s from a height of 25m. Find the time it takes to reach the ground and the speed at which it strikes.
To find the time it takes to reach the ground, we can use the formula for calculating the time taken for an object to fall a certain distance under gravity:
h = (1/2)gt^2
Where:
h = height = 25m
g = acceleration due to gravity ≈ 9.8 m/s^2
t = time taken to fall
Plugging in the values, we get:
25 = (1/2)(9.8)t^2
25 = 4.9t^2
t^2 = 25 / 4.9
t^2 = 5.102
t ≈ √5.102 ≈ 2.26 seconds
So, it takes approximately 2.26 seconds for the stone to reach the ground.
To find the speed at which the stone strikes the ground, we can use the formula for final velocity in free fall:
v = u + gt
Where:
v = final velocity (speed at which it strikes the ground)
u = initial velocity = 8 m/s
g = acceleration due to gravity ≈ 9.8 m/s^2
t = time taken to fall ≈ 2.26 seconds
Plugging in the values, we get:
v = 8 + 9.8(2.26)
v = 8 + 22.248
v ≈ 30.25 m/s
So, the speed at which the stone strikes the ground is approximately 30.25 m/s.