Answer:
The time taken by the student to climb is 12.25 seconds and work done is 2450 J.
Explanation:
Given that,
Mass of the student, m = 50 kg
The student climbs to a height of 5 meters at a constant speed.
The student's power output is 200.0 W, P = 200 W
The power of an object is given by work done divided by time taken. So,
[tex]P=\dfrac{W}{t}[/tex]
(b) W is work done,
[tex]W=mgh\\\\W=50\times 9.8\times 5\\\\W=2450\ J[/tex]
(b)
[tex]t=\dfrac{W}{P}\\\\t=\dfrac{2450}{200}\\\\t=12.25\ s[/tex]
So, the time taken by the student to climb is 12.25 seconds and work done is 2450 J.
The time taken for the student to climb the rope is 12.25 s.
The work done by the student in climbing the rope is 2,450 J.
The given parameters;
The time taken for the student to climb the rope is calculated as follows;
E = Pt
mgh = 200t
[tex]t = \frac{mgh}{200} \\\\t= \frac{50 \times 9.8 \times 5}{200} \\\\t = 12.25 \ s[/tex]
The work done by the student is obtained by applying work-energy theorem;
W = Pt
W = 200 x 12.25
W = 2,450 J
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