Question

Some gliders are launched from the ground by means of a winch, which rapidly reels in a towing cable attached to the glider. What average power must the winch supply in order to accelerate a 181-kg ultralight glider from rest to 25.7 m/s over a horizontal distance of 46.9 m? Assume that friction and air resistance are negligible, and that the tension in the winch cable is constant.

Answer 1

Answer:

$P = 1.64 \times 10^4 Watt$

Explanation:

Here we know that the glider is accelerated uniformly from rest to final speed of 25.7 m/s in total distance of d = 46.9 m

so we will have

$v_f = 25.7 m/s$

$v_i = 0$

d = 46.9

so for uniformly accelerated motion we have

$d = \frac{v_f + v_i}{2} t$

$46.9 = \frac{25.7 + 0}{2}t$

$t = 3.65 s$

now we will find the total work done given as change in kinetic energy

$W = \frac{1}{2}mv^2$

$W = \frac{1}{2}(181)(25.7^2)$

$W = 5.97 \times 10^4 J$

now power is given as

$P = \frac{W}{t}$

$P = \frac{5.97 \times 10^4}{3.65}$

$P = 1.64 \times 10^4 Watt$