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I'm having trouble distinguishing between different relative velocities.

Example: Say I'm riding my bike at a constant speed of 5 m/s in a straight line. While riding my bike I throw a baseball with an initial velocity and with an angle theta with the straight line. Now I want to figure the the initial velocity of the baseball relative to the earth. I also want to figure the initial velocity relative to me and the bike.

The plain math of calculating the velocities which includes cosines and sines is not the problem. I know that in one of the cases above I should include the speed of the bike when calculating the initial velocity, but I really don't know which one.

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1 Answers1

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It should be a simple matter of adding vectors. Suppose you are riding in the x-direction. Then your velocity relative to the earth, $u=(5,0)$

Then suppose the baseball travels at velocity $(V_x,V_y)$ relative to you, then by vector addition, the velocity of the baseball relative to the earth should be equal to the velocity of baseball relative to you + velocity of you relative to the earth. Thus the equation comes out as:

$$V_{\text(baseball.rel.earth)}=(5,0)+(V_x,V_y)=(5+V_x,V_y)$$

Of course things get more complicated when you take special relativity into account. But I don't think that is relevant in your problem here.

Muhsin Ibn Al Azeez
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Zhengyan Shi
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