Final answer:
To find the speed of the cart after the rock is dropped into it, we can use the principle of conservation of momentum. The correct answer is option a. 45.5 m/s.
Step-by-step explanation:
To find the speed of the cart after the rock is dropped into it, we can use the principle of conservation of momentum.
Before the rock is dropped into the cart, the cart's mass and velocity are given as 120kg and 47m/s, respectively. The rock's mass is 29kg.
Since there is no external force acting on the system, the total momentum before the rock is dropped is equal to the total momentum after the rock is dropped.
Momentum before = Momentum after
(120kg * 47m/s) + (29kg * 0m/s) = (120kg + 29kg) * v
Solving for v, the speed of the cart after the rock is dropped, we get v = 45.5 m/s.
Therefore, the correct answer is option a. 45.5 m/s.