a) [tex]W_1 = 2332 J[/tex], [tex]W_2= 2332 J[/tex]
The work done by the student in each trial is equal to the gravitational potential energy gained by the student:
[tex]W=mg\Delta h[/tex]
where
m = 68 kg is the mass of the student
g = 9.8 m/s^2 is the acceleration of gravity
[tex]\Delta h[/tex] is the gain in height of the student
For the first student, [tex]\Delta h = 3.5 m[/tex], so the work done is
[tex]W_1 = (68)(9.8)(3.5)=2332 J[/tex]
The second student runs up to the same height (3.5 m), so the work done by the second student is the same:
[tex]W_2 = (68)(9.8)(3.5)=2332 J[/tex]
2) [tex]P_1 = 204.6 W[/tex], [tex]P_2 = 274.4 W[/tex]
The power exerted by each student is given by
[tex]P=\frac{W}{t}[/tex]
where
W is the work done
t is the time taken
For the first student, [tex]W_1 = 2332 J[/tex] and [tex]t=11.4 s[/tex], so the power exerted is
[tex]P_1 = \frac{W_1}{t_1}=\frac{2332 J}{11.4 s}=204.6 W[/tex]
For the second student, [tex]W_2 = 2332 J[/tex] and [tex]t=8.5 s[/tex], so the power exerted is
[tex]P_2 = \frac{W_2}{t_2}=\frac{2332 J}{8.5 s}=274.4 W[/tex]
