A block moving due east collide with a block moving due west. The set of directions that is not possible after the collision is (c) One block travels northeast, and the other block travels northwest.
This problem can be solved using the law of conservation of momentum, which states the total momentums before and after collision of two objects are the same. Mathematically,
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Where:
m = mass
u = initial velocity
v = final velocity
In the given problem, one block is moving due east, and the other block is moving due west. Hence, before the collision, both objects only have velocity in horizontal components and no vertical components. Therefore, after the collision, the resultant of the velocity should also have only the horizontal component.
a. Both blocks are travelling east after the collision <---- it is possible since both objects only have horizontal component
b. Both blocks are traveling west after the collision.<---- it is possible since both objects only have horizontal component
c. One block travels northeast, and the other block travels northwest. In this case, the components of northeast velocity is due north and due east, while the components of northwest velocity is due north and due west. The resultant of velocity will have vertical (north) component, hence this set of direction is not possible.
d. One block travels southwest, and the other block travels northeast. This is possible, since the north component can be cancelled out by the south component, resulting in horizontal component only.
e. One block travels southeast, and the other block travels northwest.
This is possible, since the north component can be cancelled out by the south component, resulting in horizontal component only.
Therefore, the set of directions that is not possible is (c) One block travels northeast, and the other block travels northwest.
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