Item 10 A wagon with two boxes of gold, having total mass 300 kg, is cut loose f

Question

Item 10 A wagon with two boxes of gold, having total mass 300 kg, is cut loose from the horses by an outlaw when the wagon is at rest 50 m up a 6.0 slope (see the figure (Figure 1)). The outlaw plans to have the wagon roll down the slope and across the level ground, and then fall into a canyon where his confederates wait. But in a tree 40 m from the canyon edge wait the Lone Ranger (mass 75.0 kg) and Tonto (mass 60.0 kg). They drop vertically into the wagon as it passes beneath them. Figure 1 v of 1 300 kg 50 m 6.0 H40 m to cliff Part A f the require 5.0 8to grab the gold and jump out, will they make it before the wagon goes over the edge? The wagon rolls with negligible friction. O yes no Submit My Answers Give Up Part B When the two heroes drop into the wagon, is the kinetic energy of the system of the heroes plus the wagon conserved? O yes no Submit My Answers Give Up Part C This question will be shown after you complete previous question(s) Provide Feedback Continue

Explanation / Answer

acceleration on the incline plane = a = g Sin6 = 9.8 Sin6 = 1.024 m/s2

length of incline = d = 50 m

initial velocity at the start of incline = Vo = 0 m/s

final velocity at the bottom of incline = Vf

Using the equation ,

Vf2 = Vi2 + 2 a d

Vf2 = 02 + 2 (1.024) (50)

Vf = 10.12 m/s

Using conservation of momentum:

mc = mass of cart + gold = 300 kg

mL = mass of lone-ranger = 75 kg

mt = mass of tonto = 60 kg

momentum of cart before jumping = momentum of cart after jumping

mc Vc = (mc + mL + mt) V

300 x 10.12 = (300 + 60 + 75) V

V = 6.95 m/s

distance to be covered before reaching the edge of canyon = D = 40 m

time taken = D/V = 40 /6.95 = 5.76 sec

since the time of fall is greater than 5 sec required by loneranger and tonto, they will make it.

b)

this is a case of inelastic collision , hence the kinetic energy will not be conserved.

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