39.7k views
4 votes
Jennifer throws a baseball straight up into the air with a velocity of 16 m/s from the balcony of her apartment 20 m above the ground.

a. What is the maximum height of the baseball?
b. At this height, what is the velocity of the baseball?
c. At this height, what is the acceleration of the baseball?
d. For how long will the baseball be in the air before hitting the ground below?
e. With what velocity will the baseball hit the ground? ​

1 Answer

4 votes

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.

User Patilnitin
by
7.7k points