Question

5.The power a windmill obtains from the wind varies directly as the cube of the wind velocity. If a wind of 10 km per hr produces 10,000 units of power, how much power is produced by a wind of 15 km per hr?

Answer 1

Power α (velocity)³
⇒ P = kv³

v₁ = 10km/h, P₁ = 10,000 units
v₂ = 15 km/h, P₂ = ?

$\frac{P_2}{P_1}= \frac{v_2^3}{v_1^3} \\ \\ \Rightarrow P_2 = P_1 \times \frac{v_2^3}{v_1^3} = P_1 \times (\frac{v_2}{v_1})^3 \\ \\ \Rightarrow P_2 = 10000 \times (\frac{15}{10})^3 \\ \\ \Rightarrow P_2 = 10000 \times (1.5)^3 =10000 \times 3.375\\ \\ \Rightarrow P_2 = 33750\ units$

Power produced will be 33750 units