A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. An 810-kg helicopter rises from rest to a speed of 7.0 m/s in a time of 3.5 s. During this time it climbs to a height of 8.2 m. What is the average power generated by the lifting force?

a) M = 810 kg

b) V0 = 0 m/s

c) Vf = 7 m/s

d) t = 3.5 s

e) y = 8.2 m

24,267.6 watts

Explanation:

from the question we are given the following:

mass (m) = 810 kg

final velocity (v) = 7 m/s

initial velocity (u) = 0 m/s

time (t) = 3.5 s

final height (h₁) = 8.2 m

initial height (h₀) = 0 m

acceleration due to gravity (g) = 9.8 m/s^{2}

find the power

power = / frac{work done}[time}

and

work done = change in kinetic energy (K. E) + change in potential energy (P. E)

work done = (0.5 mv^{2} - 0.5 mu^{2}) + (mgh₁ - mgh₀)

since u and h₀ are zero the work done now becomes

work done = (0.5 mv^{2}) + (mgh₁)

work done = (0.5 x 810 x 7^{2}) + (810 x 9.8 x 8.2)

work done = 84, 936.6 joules

recall that power = / frac{work done}[time}

power = / frac{84,936.6}[3.5}

power = 24,267.6 watts