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Dynamics: Velocity of a Sphere After a Collision

Two spheres each of mass m, can slide freely on a frictionless, horizontal surface. Sphere A is moving at a speed Vo=16 ft/s when it strikes sphere B which is at rest and the impact causes sphere B to break into two pieces, each of mass m/2 Knowing that 0.7s after the collision one piece reaches point C and 0.9s after the collision the other piece reaches point D.

Determine a) the velocity of sphere A after the collision
b) the angle theta and the speeds of the two pieces after the collision

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Solution Preview

Because, after 0.7 sec the part 1 strikes the surface at C and part 2 strike with the surface after 0.9 s at point D.
let after collision their (two parts of B) velocities are v1 and v2.

Hence, along the initial direction of motion of A, distance travelled:
v1*cos(30)*0.7 = 6.3 = v2*cos(T)*0.9 ...(1)

Here, T == theta

v1 = 6.3/(0.7*sqrt(3)/2) ...

Solution Summary

Because, after 0.7 sec the part 1 strikes the surface at C and part 2 strike with the surface after 0.9 s at point D.
let after collision their (two parts of B) velocities are v1 and v2.

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