Question

# Two objects of mass 1.7 kg and 2.9 kg move with velocities (2.2, 0.5) and (2.9,...

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.

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

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