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 formula P = Fv, where P is the power, F is the force, and v is the velocity. Given that the force needed to keep the boat moving at 2.57 m/s is 165 N, we can substitute these values into the formula:

P = 165 N * 2.57 m/s
P = 423.45 Watts

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

Now, let's move on to the second question. If the resistive force of the water increases with the square of the speed, we need to calculate the new power required if the speed is increased by 50 percent.

To calculate the new power, we first need to find the new force. Since the resistive force increases with the square of the speed, we can use the formula F = k * v^2, where F is the force, v is the velocity, and k is a constant.

Let's assume k remains constant. If the speed is increased by 50 percent, the new speed would be:

New speed = 2.57 m/s + (50% of 2.57 m/s)
New speed = 2.57 m/s + (0.5 * 2.57 m/s)
New speed = 2.57 m/s + 1.285 m/s
New speed = 3.855 m/s

Now we can calculate the new force using the formula:

F = k * v^2
New force = k * (3.855 m/s)^2
New force = k * 14.859 m^2/s^2

Since the constant k is unknown, we cannot determine the exact value of the new force or power. However, we can calculate the percentage increase in power.

Percentage increase in power = (New power - Original power) / Original power * 100%
Percentage increase in power = (New force * New velocity - Original force * Original velocity) / Original force * Original velocity * 100%

Substituting the known values:

Percentage increase in power = (New force * 3.855 m/s - 165 N * 2.57 m/s) / (165 N * 2.57 m/s) * 100%

Now you can calculate the final answer using the given values and the formula above.