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5. A pool ball leaves a table with an initial horizontal velocity of 2.4 m/s and lands

0.84 m away from the table. Predict the time required for the pool ball to fall to the
ground and height of the table.

User Nulik
by
7.8k points

1 Answer

1 vote

Answer:

Step-by-step explanation:

Since the initial velocity is purely horizontal, we know that it won't affect the time taken for the ball to fall. So, we can use the equations of motion for a freely falling object to determine the time taken to fall and the height of the table.

Let's use the following equations:

h = vit + 1/2gt^2 ---(1)

vf = vi + gt ---(2)

where h is the height of the table, vi is the initial vertical velocity (which is zero), vf is the final velocity (which is the velocity with which the ball hits the ground), t is the time taken to fall, g is the acceleration due to gravity.

First, let's find the time taken for the ball to fall:

From equation (2), we have:

vf = vi + gt

vf = gt

t = vf/g

Now, we need to find vf. We know that the ball lands 0.84 m away from the table, which means that it has traveled a horizontal distance of 0.84 m. We can use this information along with the initial horizontal velocity to find the time taken for the ball to travel this distance:

d = vit

t = d/vi

t = 0.84 m / 2.4 m/s

t = 0.35 s

So, the time taken for the ball to fall is:

t = vf/g = 0.35 s

Now, we can use equation (1) to find the height of the table:

h = vit + 1/2gt^2

h = 0 + 1/2 * 9.81 m/s^2 * (0.35 s)^2

h = 0.6 m

Therefore, the height of the table is 0.6 m.

User Spannerj
by
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