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ELEN [110]
3 years ago
11

Jack (mass 59.0 kg ) is sliding due east with speed 8.00 m/s on the surface of a frozen pond. He collides with Jill (mass 47.0 k

g ), who is initially at rest. After the collision, Jack is traveling at 5.00 m/s in a direction 34.0∘ north of east. Ignore friction.
A) What is the direction of the Jill's velocity after the collision?
B) What is the magnitude of the Jill's velocity after the collision?

Physics
1 answer:
Phantasy [73]3 years ago
4 0

Answer:

Part(A): The magnitude of Jill's final velocity is \bf{6.59~m/s}.

Part(B): The direction is \bf{42.7^{0}} south to east.

Explanation:

Given:

Mass of Jack, m_{1} = 59.0~Kg

Mass of Jill, m_{2} = 47..0~Kg

Initial velocity of Jack, v_{1i} = 8.00~m/s

Initial velocity of Jill, v_{2i} = 0

Final velocity of Jack, v_{1f}  5.00~m/s

The final angle made by Jack after collision, \alpha = 34.0^{0}

Consider that the final velocity of Jill be v_{2f} and it makes an angle of \beta with respect to east, as shown in the figure.

Conservation of momentum of the system along east direction is given by

~~~~&& m_{1}v_{1i} + m_{2}v_{2i} = m_{1}v_{1f} \cos \alpha + m_{2}v_{2f}^{x}\\&or,& v_{2f}^{x} = \dfrac{m_{1}(v_{1i} - v_{1f} \cos \alpha)}{m_{2}}

where, v_{2f}^{x} is the component of Jill's final velocity along east. The direction of this component will be along east.

Substituting the value, we have

v_{2f}^{x} &=& \dfrac{(59.0~Kg)(8.00~m/s - 5.00 \cos 34.0^{0}~m/s)}{47.0~Kg}\\~~~~~&=& 4.84~m/s

Conservation of momentum of the system along north direction is given by

~~~~&& v_{2f}^{y} + v_{1f} \sin \alpha = 0\\&or,& v_{2f}^{y} = - v_{1f} \sin \alpha = (8.00~m/s) \sin 34^{0} = 4.47~m/s

where, v_{2f}^{y} is the component of Jill's final velocity along north. The direction of this component will be along the opposite to north.

Part(A):

The magnitude of the final velocity of Jill is given by

v_{2f} &=& \sqrt{(v_{2f}^{x})^{2} + (v_{2f}^{y})^{2}}\\~~~~~&=& 6.59~m/s

Part(B):

The direction is given by

\beta &=& \tan^{-1}(\dfrac{4.47~m/s}{4.84~m/s})\\~~~~&=& 42.7^{0}

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