A speed boat is required to move at a constant speed of 50 MPH. What is the power needed to overcome a resistive force of 1000 lbs from the water?

P=Fv

35hp

To calculate the power needed to overcome a resistive force, we need to use the formula: power = force × velocity. In this case, the force is 1000 lbs and the velocity is 50 MPH.

However, before we can directly use these values in the formula, we need to make sure our units are consistent. We have pounds (lbs) as the unit of force and miles per hour (MPH) as the unit of velocity. To convert lbs to Newtons (the international unit of force) and MPH to meters per second (m/s), we can use the following conversion factors:

1 lb = 0.453592 kg (to convert lbs to kg)
1 kg = 9.81 N (acceleration due to gravity)
1 mile = 1609.34 meters
1 hour = 3600 seconds

Now, let's convert the values:

Force = 1000 lbs × 0.453592 kg/lb × 9.81 N/kg (to convert lbs to Newtons)
≈ 453.59 kg × 9.81 N/kg
≈ 4448.14 N

Velocity = 50 miles/hour × 1609.34 meters/mile ÷ 3600 seconds/hour (to convert miles per hour to meters per second)
≈ 22.35 m/s

Now, we can plug these values into the formula:

Power = Force × Velocity
= 4448.14 N × 22.35 m/s
≈ 99420.89 N·m/s
≈ 99420.89 Watts

Therefore, the power needed to overcome a resistive force of 1000 lbs from the water is approximately 99420.89 Watts.