Question

The power needed to accelerate a projectile from rest to its launch speed v in a time t is 42.0 W. How much power is needed to accelerate the same projectile from rest to a launch speed of 2v in a time of t?

Answer 1

Answer:168 W

Explanation:

Given

Power needed $P=42 W$

initial Launch velocity is v

Energy of projectile when it is launched $E=\frac{1}{2}mv^2$

$Power=\frac{Energy}{time}$

$Power=\frac{E}{t}$

$42=\frac{\frac{1}{2}mv^2}{t}--------1$

Power when it is launched with 2 v

$E_2=\frac{1}{2}m(2v)^2=\frac{4}{2}mv^2$

$P=\frac{2mv^2}{t}---------2$

Divide 1 & 2 we get

$\frac{42}{P}=\frac{1}{2\times 2}$

$P=42\times 4=168 W$