Question

A car with mass M1 “ 2700 kg collides with a car of mass M2 “ 3200 kg. Before the collision car 1 has velocity ⃗v1i “p6m{s, ́14m{sqandcar2hasvelocity⃗v2i “p15m{s,0q. (a) What is the total momentum of the two cars? (6 pts) (b) Immediately after the collision the velocity of car 1 is ⃗v1f “ p14 m{s, ́6 m{sq. What is the velocity ⃗v2f of car 2 after the collision? (9 pts)

Answer #1

a)

m1 = 2700 kg

v1i = 6 i - 14 j

m2 = 3200 kg

v2i = 15 i + 0 j

Total momentum of the two cars is given as

Pi = m1 v1i + m2 v2i

Pi = (2700)(6 i - 14 j) + (3200)(15 i + 0 j)

Pi = 16200 i - 37800 j + 48000 i + 0 j

Pi = 64200 i - 37800 j

b)

m1 = 2700 kg

v1i = 6 i - 14 j

v1f = 14 i - 6 j

m2 = 3200 kg

v2i = 15 i + 0 j

v2f = ?

Using conservation of momentum

Pi = m1 v1f + m2 v2f

64200 i - 37800 j = (2700) (14 i - 6 j) + (3200) v2f

64200 i - 37800 j = 37800 i - 16200 j + (3200) v2f

26400 i - 21600 j = (3200) v2f

v2f = 8.25 i - 6.75 j

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