Question

Two objects of mass 1.7 kg and 2.9 kg move with velocities (2.2, 0.5) and (2.9, 4.0) respectively (the two numbers are the x and y components of the velocity in m/s). The two objects collide and stick together. Find the x and y components of their common final velocity and enter the magnitude (length) of the final velocity in m/s into the answer box.

Answer 1

Solution) m1 = 1.7 kg

m2 = 2.9 kg

V1 = (2.2,0.5) m/s

V1 = 2.2(i) + 0.5(j) m/s

V2 = (2.9,4) m/s

V2 = 2.9(i) + 4(j) m/s

V = ?

Applying conservation of momentum

(m1)(V1) + (m2)(V2) = ( m1 + m2 )(V)

(1.7)(2.2(i) + 0.5(j)) + (2.9)(2.9(i) + 4(j)) = ( 1.7 + 2.9)(V)

3.74(i) + 0.85(j) + 8.41(i) + 11.6(j) = (4.6)(V)

12.15(i) + 12.45(j) = 4.6(V)

V = (12.15(i) + 12.45(j))/(4.6)

V = [(12.15)/(4.6)](i) + [(12.45)/(4.6)](j)

V = 2.64(i) + 2.71(j) m/s

V = (2.64 , 2.71) m/s

Magnitude , |V| = (2.64^2 + 2.71^2)^(1/2)

|V| = 3.78 m/s