How long does it take the speedboat to reach the buoy marker?

What is the scenario given for the speedboat approaching the buoy marker?

A speedboat moving at 30.0 m/s approaches a no-wake buoy marker 100 m ahead. The pilot slows the boat with a constant acceleration of -3.50 m/s² by reducing the throttle. How long does it take the boat to reach the buoy?

Answer:

The time it takes for the speedboat to reach the buoy from the given conditions can be calculated with the motion formula. Substituting the provided values into this formula, we find that the time taken is around 6.94 seconds.

As per the scenario provided, the speedboat is moving at a velocity of 30.0 m/s towards a no-wake buoy marker located 100 meters ahead. The pilot applies a constant acceleration of -3.50 m/s² to slow down the boat before reaching the buoy.

The question inquires about the time it takes for the boat to reach the buoy under these specified conditions. To determine this, we utilize the equation of motion, which relates displacement, initial velocity, acceleration, and time.

The formula applied in this scenario is final displacement (S) = Initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)². Substituting the given values of initial velocity, acceleration, and displacement (100 meters) into this formula will allow us to solve for time (t).

By substituting the values and solving the equation, we find that the time taken for the speedboat to reach the buoy marker is approximately 6.94 seconds. This calculation considers the velocity of the speedboat and the decelerating acceleration applied by the pilot to reach a stop at the buoy marker.