If a man has an average useful power output of 31 W, what is the minimum time, in s, it would take him to lift fifty 12.3 kg boxes a height of 2.3 m.

i'm not sure how to go about it if anyone can help me
Thanks

To solve this problem, we can use the concept of work and power.

Work (W) is defined as the force (F) applied over a distance (d). In this case, the force required to lift each box is the weight of the box, which can be calculated as mass (m) multiplied by the gravitational acceleration (g).

So, the work required to lift one box a height of 2.3 m can be calculated as follows:
W = F * d
W = (m * g) * d

Now, given that the man has an average power output of 31 W, we can use the equation for power to find the time required to complete the work:
Power = Work / Time
31 W = W / Time

Substituting the work equation into the power equation:
31 W = (m * g * d) / Time

Since we are trying to find the minimum time required to lift 50 boxes, we need to divide the total work by the power output:
Total Work = 50 * W
Total Work = 50 * (m * g * d)

Now, we can rearrange the equation to solve for Time:
31 W = (50 * m * g * d) / Time

To find the minimum time, we need to determine the maximum value for the denominator. This occurs when the product of the mass, gravitational acceleration, and distance is the largest possible value.

Now, we can substitute the values given in the problem:
mass (m) = 12.3 kg
gravitational acceleration (g) ≈ 9.81 m/s²
distance (d) = 2.3 m

Plugging these values into the equation for time:
31 W = (50 * 12.3 kg * 9.81 m/s² * 2.3 m) / Time

Simplifying the equation:
31 W = 2720.85 kg⋅m²/s³ / Time

To find Time, we can rearrange the equation:
Time = 2720.85 kg⋅m²/s³ / 31 W

Calculating the result gives us:
Time ≈ 87.8 seconds

Therefore, the minimum time required for the man to lift fifty 12.3 kg boxes a height of 2.3 m is approximately 87.8 seconds.

Wb = mg = 50*12.3kg * 9.8N/kg = 6027N. = Weight of 50 boxes.

Work = Fd = 6027 * 2.3 = 13,862 Joules.

31W. = 31Joules/s.

t = 13,862J. * (1/31)s/J. = 447.2s