You are standing on a large sheet of frictionless ice and holding a large rock. In order to get off the ice, you throw the rock so it has velocity 12.0 m/sm/s relative to the earth at an angle of 35.0∘∘ above the horizontal. Your mass is 74.0 kgkg and the rock’s mass is 5.50 kgkg.Part AWhat is your speed after you throw the rock?Express your answer with the appropriate units.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typev𝑣 =nothing
Question
You are standing on a large sheet of frictionless ice and holding a large rock. In order to get off the ice, you throw the rock so it has velocity 12.0 m/sm/s relative to the earth at an angle of 35.0∘∘ above the horizontal. Your mass is 74.0 kgkg and the rock’s mass is 5.50 kgkg.Part AWhat is your speed after you throw the rock?Express your answer with the appropriate units.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typev𝑣 =nothing
Solution
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the throw is equal to the total momentum after the throw.
Before the throw, both you and the rock are stationary, so the total momentum is 0.
After the throw, the rock has a momentum of mass_rock * velocity_rock and you will have a momentum of mass_you * velocity_you.
Setting these equal gives us:
0 = mass_rock * velocity_rock - mass_you * velocity_you
We can rearrange this to solve for your velocity:
velocity_you = (mass_rock * velocity_rock) / mass_you
Substituting the given values:
velocity_you = (5.50 kg * 12.0 m/s) / 74.0 kg
This gives us the speed you will have after throwing the rock. Note that the direction of your movement will be opposite to the direction in which you threw the rock, and the angle of the throw does not affect your speed.
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