Question

A 47.0-kg girl stands on a 10.0-kg wagon holding two 23.0-kg weights. She throws the weights horizontally off the back of the wagon at a speed of 8.5 m/s relative to herself . Assuming that the wagon was at rest initially, what is the speed of the girl relative to the ground after she throws both weights at the same time?

Assuming that the wagon was at rest initially, what is the speed relative to the ground with which the girl will move after she throws the weights one at a time, each with a speed of 8.5 m/s relative to herself?

Answer 1

Part A.

When girl throws both weights at the same time,

Using Momentum conservation:

Pi = Pf

M*V = m1*V1 + 2*m2*V2

M = mass of girl + weights + wagon = 47 + 10 + 2*23 = 103 kg

V = Initial speed of wagon + girl = 0 m/sec

m1 = mass of girl + wagon = 47 + 10 = 57 m/sec

V1 = speed of girl w.r.t ground = ?

m2 = mass of weights = 2*23 kg = 46 kg

V2 = Speed of weights = 8.5 relative to girl = V1 - 8.5 (Speed w.r.t ground)

So,

103*0 = 57*V1 + 46*(V1 - 8.5)

V1 = 46*8.5/(57 + 46)

V1 = 3.80 m/sec

We have already assumed that direction of girl will be in opposite direction of weight

So Speed of girl = 3.80 m/sec

Part B.

Using above same process, but since she throws one weight at a time, So

Speed of girl after throwing first weight is suppose V1, then

Pi = Pf

M*V = m1*V1 + m2*V2

Here m1 = mass of girl + wagon + one remaining weight = 47 + 10 + 23 = 80 kg

V2 = V1 - 8.5

So

103*0 = 80*V1 + 23*(V1 - 8.5)

V1 = 23*8.5/(80 + 23)

V1 = 1.90 m/sec

Now when girl throws 2nd weight then using momentum conservation:

Pi = Pf

Suppose final speed of girl is Vf, then

M*V1 = m1*Vf + m2*V2

M = mass of girl + wagon + one weight = 80 kg

m1 = mass of girl + wagon = 47 + 10 = 57 kg

m2 = mass of weight = 23 kg

V1 = 1.90 m/sec

Vf = final speed of girl w.r.t to wagon = ?

V2 = Vf - 8.5 = speed of weight w.r.t ground

So,

80*1.90 = 57*Vf + 23*(Vf - 8.5)

Vf = (80*1.90 + 23*8.5)/(57 + 23)

Vf = 4.34 m/sec = final speed of girl w.r.t ground when she throws one weight at a time

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