Calculating Speedboat's Time and Velocity

a) How long does it take the speedboat to reach the buoy?

a) It takes 10.97 seconds for the speedboat to reach the buoy.

b) What is the velocity of the speedboat when it reaches the buoy?

b) The velocity of the boat when it reaches the buoy is 0.08 m/s.

Answer:

a) The equation we can use here is vf = vi + at where vf = final velocity, vi = initial velocity, a = acceleration, t = time taken for the object to reach its final velocity.

Initial velocity vi = 40.6 m/s

Acceleration, a = -3.7 m/s²

Distance, d = 100 m

Velocity when it reaches the buoy, vf = 0 (since it stops)

Using vf = vi + at, we can solve for t:

vf = vi + at

0 = 40.6 + (-3.7)t

3.7t = 40.6

t = 40.6 / 3.7

t = 10.97 seconds

Therefore, it takes 10.97 seconds for the speedboat to reach the buoy.

b) Since we now know the time it takes the boat to reach the buoy (t = 10.97 s), we can use the equation vf = vi + at to find its velocity when it reaches the buoy:

vf = vi + at

t = 10.97 seconds

Initial velocity, vi = 40.6 m/s

Acceleration, a = -3.7 m/s²

vf = 40.6 + (-3.7 × 10.97)

vf = 0.08 m/s

Therefore, the velocity of the boat when it reaches the buoy is 0.08 m/s.