A power boat of mass 460 kg is cruising at a constant speed of 8.9 m/s. The propeller provides a drive force of 765 N. The driver of the boat shuts off the engine, and the boat coasts to a halt. Assume -- contrary to fact -- that the resistive force due to the water is constant, independent of the boat's speed.
Well,the friction force is 765N (the driving force at constant speed), so, that stays constant during deacceleration.
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To determine the resistive force due to the water, we first need to calculate the deceleration of the boat when the engine is shut off. Knowing this deceleration, we can then use Newton's second law of motion to find the resistive force.
Step 1: Calculate the deceleration of the boat.
Newton's second law of motion states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a): F = m * a.
In this case, the only force acting on the boat when the engine is shut off is the resistive force due to the water. Therefore, we can rearrange the equation as follows: F = m * a → a = F / m.
Given:
Mass of the boat (m) = 460 kg
Force (F) = 765 N
Substituting the values into the equation, we get:
a = 765 N / 460 kg
a ≈ 1.663 m/s²
Step 2: Calculate the resistive force due to the water.
Now that we have the deceleration of the boat, we can use Newton's second law of motion again to find the resistive force. This time, we'll rearrange the equation to solve for force (F): F = m * a.
Given:
Mass of the boat (m) = 460 kg
Acceleration of the boat (a) = -1.663 m/s² (negative sign indicates deceleration)
Substituting the values into the equation, we get:
F = 460 kg * (-1.663 m/s²)
F ≈ -764 N
The negative sign indicates that the resistive force opposes the direction of motion of the boat, which is expected as it causes the boat to decelerate and eventually come to a halt. Therefore, the resistive force due to the water is approximately 764 N.