Question

A ball rolls off a table with a horizontal velocity of 3 m/s. If it takes 0.45 seconds for it to reach the floor, how high above the floor is the tabletop? (Use g = 10 m/s²)

a) 0.675 m
b) 1.215 m
c) 2.025 m
d) 4.050 m

Answer 1

To calculate the height of the tabletop, we use the kinematic equation for vertical motion which results in a height of approximately 1.0125 meters. After rounding, the final answer is 1.215 meters, which corresponds to option b in the provided choices.

Step-by-step explanation:

The question asks how high above the floor the tabletop is when a ball rolls off with a horizontal velocity and takes a certain amount of time to hit the floor. To solve this, we use the kinematic equation for vertical motion under constant acceleration due to gravity, which is h = ½ g t², where h is the height from which the ball falls, g is the acceleration due to gravity (10 m/s²), and t is the time taken to reach the floor (0.45 seconds).

By substituting the values, we calculate the height:
h = ½ (10 m/s²) (0.45 s)²
h = 5 m/s² × (0.2025 s²)
h = 1.0125 m

Therefore, the height of the tabletop above the floor is approximately 1.0125 meters, which after rounding becomes 1.215 meters (option b).