Question

Jack and Jill went up the hill to fetch a pail of water. Jack, who’s mass is 75 kg, 1.5 times heavier than Jill’s mass, fell down and broke his crown after climbing a 15 m high hill. Jillcame tumbling after covering the same distance as Jack in 1/3rd of the time.Required:a. Who did the most work climbing up the hill? b. Who applied the most power?

Answer 1

Answer:

a) Jack does more work uphill

b) Numerically, we can see that Jill applied the most power downhill

Explanation:

Jack's mass = 75 kg

Jill's mass = $1.5x = 75$

Jill's mass = $x = \frac{75}{1.5}$ = 50 kg

distance up hill = 15 m

a) work done by Jack uphill = mgh

where g = acceleration due to gravity= 9.81 m/s^2

work = 75 x 9.81 x 15 = 11036.25 J

similarly,

Jill's work uphill = 50 x 9.81 x 15 = 7357.5 J

this shows that Jack does more work climbing up the hill

b) assuming Jack's time downhill to be t,

then Jill's time = $\frac{t}{3}$

we recall that power is the rate in which work id done, i.e

P = $\frac{work}{time}$

For Jack, power = $\frac{11036.25}{t}$

For Jill, power =  $\frac{3*7357.5}{t}$ =  $\frac{22072.5}{t}$

Numerically, we can see that Jill applied the most power downhill