Question

A ball is rolled off a table with a velocity of 9.25 m/s; the table is 1.75 meters high above the floor. Determine how far from the table the ball lands?

A) 5.3 m
B) 6.0 m
C) 6.5 m
D) 7.5 m

Answer 1

Using the projectile motion equations, the ball lands approximately 5.3 meters from the table after being rolled off with a horizontal velocity of 9.25 m/s from a height of 1.75 meters.

Step-by-step explanation:

To determine how far from the table the ball lands, we can use projectile motion equations. Since the ball is rolled off the table with a horizontal velocity of 9.25 m/s, this velocity will remain constant during the flight as there is no acceleration in the horizontal direction. However, in the vertical direction, the ball is subject to gravitational acceleration, which is 9.8 m/s² downwards.

First, we calculate the time it takes for the ball to reach the floor after leaving the table:

t = sqrt(2h/g)

Substituting the given height (h = 1.75 m) and the acceleration due to gravity (g = 9.8 m/s²), we get:
t = sqrt((2 × 1.75) / 9.8) ≈ 0.596 s

Next, we use the time to find the horizontal distance (range) the ball travels:

Range = horizontal velocity × time
Range = 9.25 m/s × 0.596 s ≈ 5.51 m

Matching this result with the given options, the closest value is 5.3 m, which is option A. Therefore, the ball lands approximately 5.3 meters from the table.