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.