The original velocity of the block weighing 100 g is 40 m/s. It is struck by a block weighing 50 g traveling at 80 m/s in a direction perpendicular to the first. After the collision, the two stick together. We have to determine their final velocity.
As the second block is half the weight as that of the second but is traveling at twice the velocity, they have the same magnitude of momentum.
Let the velocity of the final block make an angle of A with the direction in which the first block was traveling.
150*v*sin A = 4000 and 150*v*cos A = 4000
Dividing the two we get tan A = 1
=> A = arc tan 1 = 45 degrees.
The magnitude of v is 4000/150*(1/sqrt 2) = 37.7 m/s
The final block made of the two block travels at 37.7 m/s in a direction making an angle of 45 degrees to the direction of the velocity of the larger block.