- #1
bobie
Gold Member
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Homework Statement
You probably know that intriguing problem: http://en.wikipedia.org/wiki/Ant_on_a_rubber_rope.
Now, suppose 2 cars A, B are speeding at vc on two roads at 60° (in a vacuum) so that their distance is at any time rt = Tt*vc. Road A points North (edit: A 0°, B 300°).
At time 10 s , at distance D =10v a bullet is shot from A at vb = vc toward (Edit: the future position of) B. (airfriction=0)
- after what time Tx the bullet will hit B? (≈14.2 s)
- what is the length L covered by the bullet? (≈21.05v )
- the shot must be fired at what angle? (≈35.65°)
- what is the right equation?
The problem is slightly different since the bullet has inertia radially but there is no rubber rope to pull it tangentially toward car B; the direction of the inertia (0°) is rougly at ≈84.35° from the direction of the bullet (≈275.65°), so the effective speed is > √2v (≈1.48v) and therefore Tx should be shorter.
2. Homework Equations ?
[tex]\frac{v_b}{v_c}\log{\left(\frac{c+vT}{c}\right)}=1 [/tex]
[tex]T_x=\frac{D}{v_b}\left(e^{v_c/v_b}-1\right) = 1* e^1 -1 = 1.7 (/1.2 )[/tex]
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