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

`P = 1.64 * 10^4 Watt`

Step-by-step 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 = (v_f + v_i)/(2) t`

`46.9 = (25.7 + 0)/(2)t`

`t = 3.65 s`

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

`W = (1)/(2)mv^2`

`W = (1)/(2)(181)(25.7^2)`

`W = 5.97 * 10^4 J`

now power is given as

`P = (W)/(t)`

`P = (5.97 * 10^4)/(3.65)`

`P = 1.64 * 10^4 Watt`