A 45.0 kg girl is standing on a 161 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat,frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.46 m/s relative to the plank. (Let thedirection the girl is moving in be positive. Indicate the direction with the sign of your answer.)(a) What is her velocity relative to the surface of ice?m/s(b) What is the velocity of the plank relative to the surface of ice?m/sNeed Help?Read It

-45.0 kg girl is standing on a 161 kg plank. The plank, originally at rest, is free to slide on a frozen lak rictionless surface. The girl begins to walk along the plank at a constant velocity of 1.46 m/s relative to lirection the girl is moving in be positive. Indicate the direction with the sign of your answer.) (a) What is her velocity relative to the surface of ice?

-45.0 kg girl is standing on a 161 kg plank. The plank, originally at rest, is free to slide on a frozen lak rictionless surface. The girl begins to walk along the plank at a constant velocity of 1.46 m/s relative to lirection the girl is moving in be positive. Indicate the direction with the sign of your answer.) (a) What is her velocity relative to the surface of ice?

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Question

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A 45.0 kg girl is standing on a 161 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat,
frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.46 m/s relative to the plank. (Let the
direction the girl is moving in be positive. Indicate the direction with the sign of your answer.)
(a) What is her velocity relative to the surface of ice?
m/s
(b) What is the velocity of the plank relative to the surface of ice?
m/s
Need Help?
Read It

Expert Solution

Step 1

Given: The mass of the girl is $45.0 kg$ .

The mass of the plank is $161 kg$ .

The initial velocity of the girl with respect to the plank is $1.46 m / s$ .

To determine: (a) Velocity of the girl relative to the surface of ice.

It is given that plank is originally at rest so initial velocity of the plank is zero, $v_{pi} = 0$ .

Let the initial velocity of the girl be $v_{gi}$ .

Th velocity of the girl with respect to plank is $v_{gp} = 1.46 m / s$

The equation for velocity is

$v_{gi} = v_{gp} + v_{pi}$ ................................................ (1)

where $v_{gi}$ is the velocity of the girl relative to ice, $v_{gp}$ is the velocity of girl relative to plank and $v_{pi}$ is the velocity of plank relative to ice.

The momentum is conserved for this girl-plank system. Initial momentum of the system is equal to final momentum.

${(m_{g} v_{gi} + m_{p} v_{pi})}_{Initial} = {(m_{g} v_{gi} + m_{p} v_{pi})}_{final}$ ............................................ (2)

where $m_{g} and m_{p}$ are the mass of the girl and the plank respectively.

The girl is initially is standing on a plank and the plank is at rest, so the initial velocity of the girl and the plank are zero.

$\begin{array}{rcl} {(m_{g} \times 0 + m_{p} \times 0)}_{Initial} & = & {(m_{g} v_{gi} + m_{p} v_{pi})}_{final} \\ 0 & = & {(m_{g} v_{gi} + m_{p} v_{pi})}_{final} \end{array}$