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.

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aristocles aristocles · Answer 1 · 2019-10-25T22:36:10+02:00

Answer:

[tex]P = 1.64 \times 10^4 Watt[/tex]

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

[tex]v_f = 25.7 m/s[/tex]

[tex]v_i = 0[/tex]

d = 46.9

so for uniformly accelerated motion we have

[tex]d = \frac{v_f + v_i}{2} t[/tex]

[tex]46.9 = \frac{25.7 + 0}{2}t[/tex]

[tex]t = 3.65 s[/tex]

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

[tex]W = \frac{1}{2}mv^2[/tex]

[tex]W = \frac{1}{2}(181)(25.7^2)[/tex]

[tex]W = 5.97 \times 10^4 J[/tex]

now power is given as

[tex]P = \frac{W}{t}[/tex]

[tex]P = \frac{5.97 \times 10^4}{3.65}[/tex]

[tex]P = 1.64 \times 10^4 Watt[/tex]