Output rating of the pump motor in watts

[howru]

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A pump is to lift 29.0 kg of water per minute through a height of 3.70 m. What output rating (watts) should the pump motor have?


An airplane pilot fell 380 m after jumping without his parachute opening. He landed in a snowbank, creating a crater 1.2 m deep, but survived with only minor injuries. Assume that the pilot's mass was 75 kg and his terminal velocity was 50 m/s.
(a) Estimate the work done by the snow in bringing him to rest.
J
(b) Estimate the average force exerted on him by the snow to stop him.
N
(c) Estimate the work done on him by air resistance as he fell.

 

[Math Is Hard]

ok, I give up. What's the answer?

 

[quicknote]

(a) To estimate the work done by the snow, we can use the equation W = mgh, where m is the mass of the pilot (75 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the crater (1.2 m). Plugging in these values, we get W = (75 kg)(9.8 m/s^2)(1.2 m) = 882 J. Therefore, the work done by the snow in bringing the pilot to rest is approximately 882 J.

(b) To estimate the average force exerted by the snow, we can use the equation F = ma, where m is the mass of the pilot (75 kg) and a is the acceleration. Since the pilot's terminal velocity is 50 m/s, we can assume that his acceleration is 0 when he reaches the snowbank. Therefore, the force exerted by the snow is 0 N.

(c) To estimate the work done by air resistance, we can use the equation W = Fd, where F is the force of air resistance and d is the distance the pilot fell (380 m). The force of air resistance can be calculated using the equation F = (1/2)ρAv^2, where ρ is the density of air (1.2 kg/m^3), A is the cross-sectional area of the pilot (assuming a human body has an area of about 0.7 m^2), and v is the velocity (50 m/s). Plugging in these values, we get F = (1/2)(1.2 kg/m^3)(0.7 m^2)(50 m/s)^2 = 1050 N. Therefore, the work done by air resistance is approximately 1050 J.