A 2.99 kg ball is dropped from the roof of a building 161.9 m high. While the ball is falling to Earth, a horizontal wind exerts a constant force of 12.3 N on the ball.
How long does it take to hit the ground> The acceleration of gravity is 9.81 m/s2.
Answer the units in s.
Also how far from the building does the ball hit the ground? Answer in units of m/s.
To find the time it takes for the ball to hit the ground, we can use the kinematic equation:
h = (1/2)gt^2
where:
h = height (161.9 m)
g = acceleration due to gravity (9.81 m/s^2)
t = time
We'll rearrange the equation to solve for t:
t^2 = (2h) / g
t = sqrt((2h) / g)
Plugging in the values, we have:
t = sqrt((2 * 161.9) / 9.81)
t ≈ 5.04 s
So it takes approximately 5.04 seconds for the ball to hit the ground.
To find the horizontal distance the ball travels before hitting the ground, we can use the following equation:
d = v * t
where:
d = distance
v = horizontal velocity
t = time
The horizontal velocity remains constant, as there is no force acting in the horizontal direction. So, v = 0 m/s.
Thus, the distance the ball travels is:
d = 0 * 5.04
d = 0 m
Therefore, the ball hits the ground directly below the building, so the distance from the building is 0 meters.