Interesting physics problem requireing more trigonometry knowlege than I posess.

[CaptainBlood]

Agent 007 has just stolen some blueprints from Dr.

No, whose henchmen are now in vigorous pursuit of

Mr. Bond. He sees his best chance of escape: a

wooden boxcar. In a moment, James is in the car and

moving along a straight railroad track at speed v1 . A

sniper fires a bullet (initial speed v2 ) at it from a high-

powered rifle. The bullet passes through both length-

wise walls of the car, its entrance and exit holes being

exactly opposite each other as viewed from within the

car. Assume that the bullet is not deflected upon en-

tering the car, but that its speed decreases by 20%.

Show that the direction, relative to the track, from

which the bullet is fired is given by

θ = π − arccos ( 5v1 / 4v2 )

 

(Why don’t you need to know the width of the box-

car?)

 

From the information given, we know that the triangle that is being formed by the trajectories of the v1 and (.8) v2 is a right triangle in which sin theta = 5v1 / 4v2. We also know that the trajectory of the bullet before it reaches the boxcar is given by sin theta = v1/v2, so the combined trajectory is the vector sum of v2 and (.8)v2 which would give us the angle theta that we are looking for, but then I don't know how to proceed. Then I thought that that is not right because in the problem it states that the trajectory of the bullet didn't change, so while the bullet traveled at (.8)v2 speed the cart traveled enough distance for the bullet to hit the other wall at the middle point. That means that when the bullet is traveling along a hypotenuse with the speed (.8)v2 the cart is traveling up at speed v1 until they meet, thus the width of the cart doesn't matter. Does what I'm saying make sense? How should I approach this problem?

[CaptainBlood]

Don't worry about it I solved it already.