The motor of a ski boat generates an average power of 5.83 × 104 W when the boat is moving at a constant speed of 17.4 m/s. When the boat is pulling a skier at the same speed, the engine must generate an average power of 8.45 × 104 W. What is the tension in the tow rope that is pulling the skier?
To find the tension in the tow rope, we can use the equation for power:
Power = Force × Velocity
When the boat is moving at a constant speed, the power generated by the motor is equal to the power required to overcome the drag:
Power = drag force × boat velocity
So, when the boat is moving at a constant speed of 17.4 m/s, the power generated by the motor is 5.83 × 10^4 W.
Now, let's find the drag force on the boat when it is moving at 17.4 m/s:
Drag Force = Power / Velocity
Drag Force = 5.83 × 10^4 W / 17.4 m/s
Next, when the boat is pulling a skier at the same speed of 17.4 m/s, the power generated by the motor is 8.45 × 10^4 W.
Now, let's find the total force acting on the boat when it is pulling the skier:
Total Force = Power / Velocity
Total Force = 8.45 × 10^4 W / 17.4 m/s
Finally, to find the tension in the tow rope, we need to subtract the drag force from the total force:
Tension = Total Force - Drag Force
Tension = (8.45 × 10^4 W / 17.4 m/s) - (5.83 × 10^4 W / 17.4 m/s)
Simplifying the equation will give you the value for the tension in the tow rope.