A lab cart with a mass of 15 kilograms is moving with constant velocity, v , along a straight horizontal track. A student drops a 2 kilograms mass into it from directly above, and the cart continues moving. Which equation best represents the horizontal momentum in this situation?
Answer
A
15 v sub i plus 2 v sub f is equal to 15 times 0 plus 2 v sub i
B
15 times 0 plus 2 v sub i is equal to open paren 15 plus 2 close paren times v sub f
C
15 v sub i plus 2 times 0 is equal to open paren 15 plus 2 close paren times v sub f
D
15 v sub i plus 2 times 0 is equal to 15 v sub f plus 2 times 0
Explanation
Horizontal momentum is conserved because there is no net external horizontal force. Initially, the 15-kilogram cart moves at velocity v_i, while the 2-kilogram mass is dropped vertically and has zero horizontal velocity, so the initial horizontal momentum is 15v_i + 2(0). After the mass lands in the cart, they move together at v_f, giving final momentum (15 + 2)v_f. This is choice C.
AI-written and checked against the verified answer.