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.