A 4.05 kg ball is dropped from the roof of a building 171.4 m high. While the ball is falling to Earth, a horizontal wind exerts a constant force of 12.5 N on the ball. How long does it take to hit the ground? The acceleration of gravity is 9.81 m/s^2.
oops.. i mean how do you the distance it fell from the building?
I feel satisfied after rdeanig that one.
To find the time it takes for the ball to hit the ground, we can use the equations of motion. The key equation here is the equation for vertical motion:
s = ut + 0.5at^2
Where:
- s is the vertical displacement (in this case, -171.4 m since the ball is dropping downwards)
- u is the initial velocity (which is 0 as the ball is dropped)
- a is the acceleration due to gravity (-9.81 m/s^2, negative because it is acting downwards)
- t is time (which is what we are trying to find)
Rearranging the equation, we get:
t = √((2s)/a)
Substituting the values into the equation:
t = √((2 * -171.4 m) / -9.81 m/s^2)
Note that we have used -171.4 m for s and -9.81 m/s^2 for a because they are both acting downwards.
Simplifying the equation, we get:
t = √(34.85 s^2)
t ≈ 5.90 s
Therefore, it takes approximately 5.90 seconds for the ball to hit the ground.