Really though relative motion/momentum question

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In summary, a 45 kg girl standing on a 150 kg plank begins to walk at a constant velocity of 1.5 m/s to the right relative to the plank on a frictionless surface. Her velocity relative to the surface of the ice is 1.15 m/s, while the plank's velocity relative to the surface of the ice is 0.346 m/s. This is due to the conservation of momentum, as the center of mass of the girl-plank system must remain stationary since there is no outside force on the system.
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Okay, really tough for me atleast.
A 45 kg girl is standing on a 150 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 1.5 m/s to the right relative to the plan. a) what is her velocity relative to the surface of the ice? B) What is the velocity of the plank relative to the surface of the ice?
Answers are 1.15 m/s and 0.346 m/s
edit: title = tough*
 
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Conservation of momentum. Or that the center of mass of the girl-plank system must remain stationary since there is no outside force on the system.

Be careful with speeds. If the plank's speed, relative to the ice is v, then the girl's speed relative to the ice is (1.5+ v) m/s (of course, the plank moves opposite to the girl so v will be negative). The girl's momentum, then, is
45(1.5+ v) kgm/s and the plank's is 150 v kgm/s. By conservation of momentum, 45(1.5+ v)+ 150v= 0.
 
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Got it... Thanks!
 

1. What is relative motion and how does it work?

Relative motion refers to the movement of an object in relation to another object. It takes into account the perspective of the observer and how their position affects their perception of motion. An object's speed and direction can appear different depending on the observer's frame of reference.

2. How is relative motion different from absolute motion?

Absolute motion is the movement of an object in relation to a fixed point or reference frame, such as the Earth. It does not take into account the perspective of the observer. Relative motion, on the other hand, considers the observer's frame of reference and their point of view.

3. What is momentum and how is it related to relative motion?

Momentum is a measure of an object's motion and is calculated by multiplying its mass and velocity. In terms of relative motion, the momentum of an object can change depending on the perspective of the observer. For example, an object may have a different momentum when viewed from a stationary observer compared to an observer who is also moving.

4. How does Newton's laws of motion apply to relative motion?

Newton's laws of motion still apply to relative motion. The first law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The second law explains how a force affects the motion of an object by changing its momentum. The third law states that for every action, there is an equal and opposite reaction, which can also affect relative motion.

5. How is relative motion used in real life?

Relative motion has many practical applications in everyday life. For example, it is used in navigation, such as determining the speed and direction of a moving vehicle in relation to other objects. It is also used in sports, such as calculating the speed and trajectory of a ball in motion. In addition, relative motion is important in understanding the effects of speed and direction on collisions and interactions between objects.

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