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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?

Respuesta :

Answer:

T = 4517.48 N

Explanation:

It is given that,

Average power of the motor, [tex]P_1=2.74\times 10^4\ W[/tex]

Speed of the boat, [tex]v_1=14.3\ m/s[/tex]

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

[tex]P=T\times v[/tex]

[tex]T=\dfrac{P_1}{v_1}[/tex]

[tex]T=\dfrac{2.74\times 10^4}{14.3}[/tex]

T = 1916.08 N

Average power generated by the engine, [tex]P_2=9.2\times 10^4\ W[/tex]

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

[tex]P=T\times v[/tex]

[tex]T=\dfrac{P_2}{v_2}[/tex]

[tex]T=\dfrac{9.2\times 10^4}{14.3}[/tex]

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