Question

A baseball is dropped from the top of a 85 m tall building. Ignoring air resistance, how fast will it hit the ground?

Answer 1

Since the baseball is dropped from rest (i.e., initial velocity of 0 m/s), we can use the kinematic equation that describes the relationship between distance, acceleration due to gravity, time, and final velocity:

distance = (1/2) * acceleration * time^2 + initial_velocity * time

Since the baseball starts from rest, the initial velocity is 0. We know the height of the building is 85 m, the acceleration due to gravity is 9.81 m/s^2, and we want to find the final velocity just before it hits the ground. We can use the kinematic equation to solve for time and then use time to find the final velocity:

distance = (1/2) * acceleration * time^2

85 = (1/2) * 9.81 * time^2

time^2 = 17.328

time = 4.166 s

Now we can use the kinematic equation to find the final velocity:

final_velocity = acceleration * time

final_velocity = 9.81 * 4.166

final_velocity = 40.9 m/s

Therefore, ignoring air resistance, the baseball will hit the ground with a velocity of approximately 40.9 m/s.

Answer 2

We can solve this problem using the kinematic equation for free fall:

h = 1/2 gt^2

where h is the initial height (85 m), g is the acceleration due to gravity (-9.8 m/s^2), and t is the time it takes for the ball to hit the ground. Solving for t, we get:

t = sqrt(2h/g)
t = sqrt(2(85 m)/9.8 m/s^2)
t = 4.2 s

Now that we know the time it takes for the ball to hit the ground, we can use another kinematic equation to find its final velocity:

v = gt
v = 9.8 m/s^2 x 4.2 s
v = 41.2 m/s

Therefore, the ball will hit the ground with a velocity of approximately 41.2 m/s