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# Physics with calculus word problem please!?

Hockey puck B rests on a smooth ice surface and is struck by a second puck A, which has the same mass. Puck A is initially traveling at 14.3 m/s and is deflected 30.0 ∘ from its initial direction. Assume that the collision is perfectly elastic.

1.Find the final speed of the puck B after the collision.

2.Find the final speed of the puck A after the collision.

3.Find the direction of B's velocity after the collision.

### 1 Answer

- NCSLv 74 weeks ago
For an elastic collision between equal masses, it can be shown that the angle between the post-collision velocities is 90º. So I'll start with

3. Θ = -60º

conserve momentum vertically:

0 = M*v*sin30º + M*u*sin-60º → mass M cancels

and v is the velocity of puck A

v = 1.732u

and horizontally, substituting for v:

M*14.3m/s = M*1.732u*cos30º + M*u*cos-60º = M*2u

1. u = ½*14.3m/s = 7.15 m/s ◄ puck B

2. v = 1.732*7.15m/s = 12.4 m/s ◄ puck A

Had the masses not been equal, then in addition to the two momentum equations you'd have a conservation of energy equation. The three equations together would allow you to solve for v, u and Θ.

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