Answer:
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.
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;
[tex]P.E = mgh\\\\P.E = 75 \times 9.8 \times 15.24 \\\\P.E =11,201.4 \ J[/tex]
The time taken for the student to travel up the three stairs is calculated as follows;
[tex]E = Pt\\\\t = \frac{E}{P} \\\\t = \frac{11,201.4}{500} \\\\t = 22.4 \ s[/tex]
Thus, the time taken for the student to travel up the three stairs is 22.4 s.
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