Question

A man produces a power output P as he lifts a weight of 200 newtons to height H in time T. If a second person is to lift the same weight to height of 2H in time T/2 he would produce a power output of

(1) P/4 (3) 2P (2) P/2 (4) 4P

Answer 1

(4) 4P.

Step-by-step explanation:
The work done in lifting a weight of 200 newtons to a height H is given by:

W = F * d = 200 * H

The time taken to lift the weight to a height H is T, so the power output is:

P = W / T = (200 * H) / T

Now, the second person has to lift the same weight to a height of 2H in half the time, which means T/2. The work done is:

W = F * d = 200 * 2H = 400H

The time taken is T/2, so the power output is:

P' = W / (T/2) = (400H) / (T/2) = 800H/T

Comparing P and P', we get:

P' = 4P

Therefore, the second person would produce a power output of 4P. Answer: (4) 4P.

Answer 2

Step-by-step explanation:

The work done by the first person in lifting the weight to a height H is given by:

W = F × d = 200 × H

The power output P of the first person is then given by:

P = W / T = (200 × H) / T

To lift the same weight to a height of 2H in time T/2, the second person would have to do twice the work done by the first person, since work done is equal to force times distance. Therefore, the work done by the second person is given by:

W = 2 × (200 × 2H) = 800H

The power output of the second person is then given by:

P' = W / (T/2) = (800H) / (T/2) = (800H × 2) / T = 1600H / T

Comparing the power output of the first person (P) and the second person (P'), we have:

P' / P = (1600H / T) / (200H / T) = 8

Therefore, the power output of the second person is 8 times the power output of the first person. So, the correct option is (3) 2P.