A boat moves through the water with two forces acting on it. One is a 1,950-N forward push by the water on the propeller, and the other is a 1,000-N resistive force due to the water around the bow.
(a) What is the acceleration of the 1,500-kg boat?
m/s 2
(b) If it starts from rest, how far will the boat move in 22.5 s?
m
(c) What will its velocity be at the end of that time?
m/s
To answer these questions, we need to use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
(a) To find the acceleration of the boat, we need to calculate the net force acting on it. The net force is the difference between the forward push and the resistive force. In this case, the net force is:
Net Force = Forward Push - Resistive Force
Net Force = 1,950 N - 1,000 N
Net Force = 950 N
Now, we can calculate the acceleration using Newton's second law:
Acceleration = Net Force / Mass
Acceleration = 950 N / 1,500 kg
Acceleration ≈ 0.633 m/s^2
Therefore, the acceleration of the boat is approximately 0.633 m/s^2.
(b) To find how far the boat will move in 22.5 seconds, we can use the equation of motion:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2
Since the boat starts from rest, the initial velocity is zero. Plugging in the values:
Distance = 0 * 22.5 s + (1/2) * 0.633 m/s^2 * (22.5 s)^2
Distance = 0 + (1/2) * 0.633 m/s^2 * 506.25 s^2
Distance ≈ 160.197 m
Therefore, the boat will move approximately 160.197 meters in 22.5 seconds.
(c) Finally, to find the velocity of the boat at the end of that time, we can use the equation of motion:
Final Velocity = Initial Velocity + Acceleration * Time
Since the boat starts from rest, the initial velocity is zero. Plugging in the values:
Final Velocity = 0 + 0.633 m/s^2 * 22.5 s
Final Velocity ≈ 14.187 m/s
Therefore, the velocity of the boat at the end of 22.5 seconds is approximately 14.187 m/s.