A block at rest is hit by another block coming in at 5 m/s. After the collision

Question

A block at rest is hit by another block coming in at 5 m/s. After the collision they stick together and move at 3 m/s. What is the ratio of their masses? At a street corner two cars collide. The first one, 1200 lb, is moving due west at 30 mph. The second, 1500 lb, is moving due south at 45 mph. If the cars got tangled up together, how fast will they be moving and in what direction? Two blocks of mass 5 and 4 kg are involved in an elastic collision. The 5 kg block is at rest and the other hits it head on going at 2 m/s. What are their velocities after the collision? [v_4 = -2/9 m/s, v_5 = 16/9 m/s] What would be their velocities if both blocks were 5 kg each?

Explanation / Answer

1.

m1 = mass of block at rest

v1i = initial velocity of block at rest = 0 m/s

m2 = mass of block moving initially

v2i = initial velocity of block moving = 5 m/s

V = velocity of the combination after the collision = 3 m/s

using conservation of momentum

m1 v1i + m2 v2i = (m1 + m2) V

(0) m1 + m2 (5) = (m1 + m2) (3)

2 m2 = 3 m1

m1 = 2 m2 /3

2)

consider east-west direction along X-axis and north-south direction along Y-axis

m1 = mass of first 1 = 1200 lb

V1i = initial velocity of first 1 = - 30 i + 0 j

m2 = mass of second 1 = 1500 lb

V2i = initial velocity of second 1 = 0 i - 45 j

V = final velocity

using conservation of momentum

m1 V1i + m2 V2i = (m1 + m2) V

1200 (- 30 i + 0 j) + (1500) (0 i - 45 j) = (1200 + 1500) V

2700 V = - 36000 i - 67500 j

V = - 13.33 i - 25 j

magnitude : = sqrt((- 13.33)2 + (- 25)2) = 28.33 mph

direction : = tan-1(25/13.33) = 61.9 deg south of west

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