Question

The motor of a ski boat generates an average power of 2.74 × 10^4 W when the boat is moving at a constant speed of 14.3 m/s. When the boat is pulling a skier at the same speed, the engine must generate an average power of 9.20 × 10^4 W. What is the tension in the tow rope that is pulling the skier?

Answer 1

T = 4517.48 N

Step-by-step explanation:

It is given that,

Average power of the motor,
`P_1=2.74* 10^4\ W`

Speed of the boat,
`v_1=14.3\ m/s`

Force or tension acting on the motor at this point is given by :

`P=T* v`

`T=(P_1)/(v_1)`

`T=(2.74* 10^4)/(14.3)`

T = 1916.08 N

Average power generated by the engine,
`P_2=9.2* 10^4\ W`

Force or tension acting on the motor at this point is given by :

`P=T* v`

`T=(P_2)/(v_2)`

`T=(9.2* 10^4)/(14.3)`

T = 6433.56 N

So, the tension in the tow rope that is pulling the skier is, T = 6433.56 N - 1916.08 N = 4517.48 N