How to Calculate Time and Velocity of a Speedboat Approaching a Buoy?
a) How long does it take the boat to reach the buoy?
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 23.50 m/s2 by reducing the throttle.
b) What is the velocity of the boat when it reaches the buoy?
The boat takes about 6.58 seconds to reach the buoy and the velocity of the boat when it reaches the buoy is 0 m/s.
Answer:
a) The boat takes about 6.58 seconds to reach the buoy.
b) The velocity of the boat when it reaches the buoy is 0 m/s.
The subject of this question is Physics, specifically motion, acceleration, and velocity under constant acceleration.
Firstly, we need to find the time it takes for the boat to reach the buoy. We will use the kinematic equation: d = vt + 0.5at^2, where d, v, a, and t represent the distance, initial velocity, acceleration, and time, respectively.
This equation allows us to solve for t (time), giving us t = √((2d)/a), by rearranging and assuming initial velocity (v) is 0 given the boat decelerates to a stop. Plugging in the numbers: t = √((2*100m)/23.5m/s^2) = 6.58s. Hence, it takes about 6.58 seconds for the boat to hit the buoy.
b) To find the velocity of the boat when it reaches the buoy, we use another kinematic equation: v = u - at, where v is final velocity, u is initial velocity, a is acceleration, and t is time.
So, v = 30.0m/s - (23.5m/s^2 * 6.58s) = -24.63m/s, which can be interpreted as the boat going 24.63 m/s backwards. This is not feasible in reality, so when the boat reaches the buoy, its velocity is 0 m/s.