Speedboat Acceleration Calculation

What is the initial velocity of the speedboat in this scenario?

28 m/s

What is the acceleration of the speedboat as it approaches the buoy marker?

4 m/s2

How far is the buoy marker from the speedboat's initial position?

91 m

What is the final velocity of the speedboat when it reaches the buoy?

7.5 m/s

Answer:

The final velocity of the speedboat when it reaches the buoy is 7.5 m/s.

When a speedboat is moving at 28 m/s and approaches a buoy marker that is 91 m ahead, the pilot slows down the boat with a constant acceleration of 4 m/s2. The goal is to calculate the velocity of the speedboat when it reaches the buoy.

To solve this problem, we can use one of Newton's equations of motion:

v^2 = u^2 + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
s = distance traveled

Given data:
Initial velocity (u) = 28 m/s
Acceleration (a) = -4 m/s2 (negative because it's decelerating)
Distance to buoy marker (s) = 91 m

Calculating:
v^2 = 28^2 + 2 * (-4) * 91
v^2 = 784 + -728 = 56
v = √56 = 7.5 m/s

Therefore, the final velocity of the speedboat when it reaches the buoy is 7.5 m/s.