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

a) Jack does more work uphill

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

Step-by-step explanation:

Jack's mass = 75 kg

Jill's mass =
`1.5x = 75`

Jill's mass =
`x = (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 =
`(t)/(3)`

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

P =
`(work)/(time)`

For Jack, power =
`(11036.25)/(t)`

For Jill, power =
`(3*7357.5)/(t)` =
`(22072.5)/(t)`

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