Answer:
Step-by-step explanation:
To solve this problem, we can use the kinematic equations of motion for an object in free fall.
a) The maximum height of the baseball can be found using the formula:
h = h0 + v0t - (1/2)gt^2
where h0 is the initial height of the baseball (20 m), v0 is the initial velocity of the baseball (16 m/s), g is the acceleration due to gravity (9.81 m/s^2), and t is the time taken for the ball to reach maximum height (which can be found using v = v0 - gt = 0).
v0 = 16 m/s
g = 9.81 m/s^2
v = 0 m/s (at maximum height)
v = v0 - gt
t = v0/g
h = h0 + v0t - (1/2)gt^2
h = 20 m + (16 m/s)(16 m/s) / (2*9.81 m/s^2)
h = 20 m + 12.95 m
h = 32.95 m
Therefore, the maximum height of the baseball is 32.95 m.
maximum height, the velocity of the baseball is 0 m/s.
c) At the maximum height, the acceleration of the baseball is equal to the acceleration due to gravity, which is -9.81 m/s^2 (negative because it is directed downward).
d) The time taken for the ball to reach maximum height is given by:
v = v0 - gt
0 m/s = 16 m/s - 9.81 m/s^2*t
t = v0/g = 16 m/s / 9.81 m/s^2 = 1.63 s (approx)
The total time the ball is in the air is twice the time it takes to reach maximum height, so the time it takes to hit the ground is:
t_total = 2t = 2(1.63 s) = 3.26 s
Therefore, the ball is in the air for 3.26 seconds before hitting the ground.
e) The velocity with which the ball hits the ground can be found using the formula:
v = v0 - gt
where v0 is the initial velocity of the ball (16 m/s), g is the acceleration due to gravity (-9.81 m/s^2), and t is the time taken for the ball to hit the ground (3.26 s).
v = 16 m/s - 9.81 m/s^2 * 3.26 s
v = -21.13 m/s
The negative sign indicates that the ball is moving downward, and the magnitude of the velocity is 21.13 m/s.
Therefore, the baseball hits the ground with a velocity of 21.13 m/s directed downward.