How Long Does It Take for a Speedboat to Reach a No-Wake Buoy Marker?

Calculation of Time Taken for the Boat to Reach the Buoy:

Final answer: The total time taken is approximately 6.83 seconds for the boat to reach the buoy.

Explanation:

To find the time it takes for the boat to reach the buoy, we can use the equation:

d = v₀t + 0.5at²

Where:

d = displacement (100 m)

v₀ = initial velocity (32.0 m/s)

a = acceleration (-3.5 m/s²)

t = time

Plugging in the values, we get:

100 = (32.0)t + 0.5(-3.5)(t²)

After rearranging the equation and solving for t using the quadratic formula, we find that t ≈ 6.83 seconds. Therefore, it takes approximately 6.83 seconds for the boat to reach the buoy.