Velocity Calculation of a Speedboat

What is the velocity of the boat when it reaches the buoy?

A speedboat moving at 31.0 m/s approaches a buoy marker 86.0 m ahead. The pilot slows the boat with a constant acceleration of -3.70 m/s2 by reducing the throttle.

Answer:

The velocity of the boat when it reaches the buoy is 21.2 m/s.

To find the velocity of the boat when it reaches the buoy, we can use the equation:

v^2 = u^2 + 2as

Where:

v is the final velocity

u is the initial velocity

a is the acceleration

s is the distance traveled

In this case, the initial velocity (u) is 31.0 m/s, the acceleration (a) is -3.70 m/s^2, and the distance traveled (s) is 86.0 m.

Plugging these values into the equation, we have:

v^2 = (31.0 m/s)^2 + 2(-3.70 m/s^2)(86.0 m)

v^2 = 961.0 m^2/s^2 - 509.6 m^2/s^2

v^2 = 451.4 m^2/s^2

Taking the square root of both sides, we get:

v = sqrt(451.4 m^2/s^2)

v = 21.2 m/s

Therefore, the velocity of the boat when it reaches the buoy is 21.2 m/s.