A force of 165 N is needed to keep a small boat moving at 2.57 m/s. What is the power required to keep the boat moving at the steady speed?

>> I understand that P=Fv but I don't understand the second question.

If the resistive force of the water increases with the square of the speed, what power is required if the speed is increased by 50 percent?

To find the power required to keep the boat moving at a steady speed, we can use the equation P = F * v, where P is the power, F is the force required, and v is the velocity of the boat.

In this case, the force required to keep the boat moving at a velocity of 2.57 m/s is given as 165 N.

Therefore, we can calculate the power required by substituting the given values into the equation:

P = 165 N * 2.57 m/s
P = 423.45 Watt (W)

So, the power required to keep the boat moving at a steady speed of 2.57 m/s is 423.45 W.

Now, let's move on to the second question.

If the resistive force of the water increases with the square of the speed, and we want to find the power required when the speed is increased by 50 percent, we need to follow these steps:

1. Calculate the original speed: The original speed is given as 2.57 m/s.

2. Calculate the increased speed: To find the increased speed, we need to add 50 percent of the original speed to the original speed.
Increased speed = original speed + (50% of original speed)
Increased speed = 2.57 m/s + (0.5 * 2.57 m/s)
Increased speed = 2.57 m/s + 1.285 m/s
Increased speed = 3.855 m/s

Now that we know the increased speed, we can calculate the resistive force at this new speed.

3. Calculate the new resistive force: As per the problem, the resistive force of the water increases with the square of the speed. Therefore, we can use the formula: New force = Original force * (New speed / Original speed)^2

New force = 165 N * (3.855 m/s / 2.57 m/s)^2
New force = 165 N * (1.5)^2
New force = 165 N * 2.25
New force = 371.25 N

Now that we have the new force, we can calculate the power required to maintain this new speed.

4. Calculate the new power required: We can use the same power equation to find the new power.
New power = New force * new speed
New power = 371.25 N * 3.855 m/s
New power = 1430.74 Watt (W)

So, the power required to keep the boat moving at the increased speed of 50 percent (3.855 m/s) is approximately 1430.74 W.