Question

A ball of 2 kg travels in the x direction with a velocity of 4 m/s. It collides with a ball of mass 3 kg which is initially at rest. After the collision, the first ball travels at a velocity of 2.5 m/s at an angle of 30 degrees from the x axis. What is the velocity of the second ball? NOTE: what if they stuck together? What kind of collision would that be?

Answer #1

here,

m1 = 2 kg is at u1 = 4 i m/s

m2 = 3 kg

v1 = 2.5 * (cos(30) i + sin(30) j)

v1 = 2.17 i m/s + 1.25 j m/s

let the final speed of seccond be v2

using conservation of momentum

m1 * u1 = m1 * v1 + m2 * v2

2 * 4 i + 2 * ( 2.17 i + 1.25 j) * 3 * v2

solving for v2

v2 = 1.22 i - 0.833 j m/s

the magnitude of velocity , |v2| = sqrt(1.22^2 + 0.833^2) = 1.48 m/s

theta = arctan(0.833/1.22) = 34.3 degreee below the +x axis

IF they stuck together

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