Question

Object A (mass 10.0 kg) is moving due east with a velocity of v⃑A0 = 8.00 m s EAST. Object B (mass 18.0 kg) is moving due north with a velocity of v⃑B0 = 5.00 m s NORTH. They collide and stick together. Find the magnitude and direction (in terms of an angle) of the two-object system following the collision.

Answer 1

here,

mass of object , mA = 10 kg has initial speed , uA = 8 m/s i

mass of object B , mB = 18 kg has initial speed , uB = 5 m/s j

let the final speed after the collison be v

using conservation of momentum

mA * uA + mB * uB = (mA + mB) * v

10 * 8 i + 18 * 5 j = ( 10 + 18) * v

solving for v

v = (2.86 i + 3.21 j) m/s

the magnitude of final velocity , |v| = sqrt(2.86^2 + 3.21^2) = 4.3 m/s

the anfle of velocity , theta = arctan(3.21 /2.86) = 48.3 degree North of East