Question

A golf ball is thrown downward with a velocity of -1.98 m/s. The golf ball hits the ground with a velocity of -32.87 m/s. What was the vertical displacement of the ball? (Round answers to two decimal places.)

a) 30.89 meters
b) 34.85 meters
c) 33.89 meters
d) 31.76 meters

Answer 1

The vertical displacement of the golf ball is approximately -33.89 meters. The correct answer is c) 33.89 meters.

Step-by-step explanation:

To calculate the vertical displacement of the golf ball, we need to find the difference between its initial and final velocities.

The initial velocity is -1.98 m/s and the final velocity is -32.87 m/s.

Velocity is defined as the change in position over time, so we can calculate the time it takes for the ball to reach the ground using the equation:

Final Velocity = Initial Velocity + (Acceleration × Time)

Since the ball is thrown vertically downwards, the acceleration due to gravity is -9.8 m/s². By rearranging the equation, we get:

Time = (Final Velocity - Initial Velocity) / Acceleration

Substituting the given values, we have:

Time = (-32.87 - (-1.98)) / -9.8

Solving this equation gives us a time of approximately 3.25 seconds. Next, we can use the time to calculate the vertical displacement of the ball using the equation:

Displacement = Initial Velocity × Time + (1/2) × Acceleration × Time²

Substituting the given values, we have:

Displacement = -1.98 × 3.25 + (1/2) × -9.8 × (3.25)²

Solving this equation gives us a displacement of approximately -33.89 meters. Since displacement is a vector quantity, the negative sign indicates that the ball is moving downwards.

Therefore, the correct answer is c) 33.89 meters.