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.