A 75 kg student walks up three flights of stairs, a vertical height of about 50 ft. If the magnitude of the average rate at which the gravity force does work on the student equals 500 W, how long would it take the student to travel up the three flights of stairs?

The time taken for the student to travel up the three stairs is 22.4 s.

The given parameters;

The gravitational potential energy of the student due to vertical position of the three stairs is calculated as;

The time taken for the student to travel up the three stairs is calculated as follows;

Thus, the time taken for the student to travel up the three stairs is 22.4 s.

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22.4 s

Explanation:

The following data were obtained from the question:

Mass (m) = 75 Kg

Height (h) = 50 ft

Power (P) = 500 W

Acceleration due to gravity (g) = 9.8 m/s²

Time (t) =?

Next, we shall convert 50 ft to metres (m). This can be obtained as follow:

1 ft = 0.3048 m

Therefore,

50 ft = 50 ft × 0.3048 m / 1 ft

50 ft = 15.24 m

Thus, 50 ft is equivalent 15.24 m.

Next, we shall determine the energy used by the student to walk up three flights of stairs. This can be obtained as follow:

Mass (m) = 75 Kg

Height (h) = 15.24 m

Acceleration due to gravity (g) = 9.8 m/s²

Energy (E) =?

E = mgh

E = 75 × 9.8 × 15.24

E = 11201.4 J

Finally, we shall determine the time taken for the student to travel up the three flights of stairs. This can be obtained as follow:

Power (P) = 500 W

Energy (E) = 11201.4 J

Time (t)

Power (P) = Energy (E) / Time (t)

500 = 11201.4 /t

Cross multiply

500 × t = 11201.4

Divide both side by 500

t = 11201.4 /500

t = 22.4 s

Therefore, it will take the student 22.4 s to travel up the three flights of stairs.

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