Exciting Speedboat Adventure: How Long to Reach the Buoy?

Wondering about the speedboat's journey to the buoy?

A speedboat moving at 32.0 m/s approaches a no-wake buoy marker 100 m ahead. The pilot slows the boat with a constant acceleration of -3.5 m/s² by reducing the throttle. How long does it take the boat to reach the buoy?

Answer:

The boat takes approximately 9.14 seconds to reach the buoy.

Embark on an exhilarating speedboat adventure as we explore the journey of a speedboat approaching a no-wake buoy marker! The pilot bravely navigates the waters, slowing down the boat with a thrilling acceleration. But how long does it take for the boat to reach the buoy?

To find the answer, we utilize the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity (u) is 32.0 m/s, the acceleration (a) is -3.5 m/s² (negative due to deceleration), the final velocity (v) is 0 m/s (as the boat stops at the buoy).

By rearranging the equation, we can determine the time taken for the boat to reach the buoy: t = (v - u) / a. Substituting the values, we find: t = (0 - 32.0) / -3.5 = 9.143 seconds. Therefore, it takes approximately 9.14 seconds for the boat to reach the buoy in this thrilling speedboat adventure!