I need help with the final part of a long momentum problem
This question has 4 parts. I managed to do a) to c) but I can't figure out d) at all.
A student is throwing bricks at his physics teacher. The bricks have a mass of 2 kg and the student can throw them with a speed of 10 m/s. The teacher is standing on a frozen lake so there is no friction and his mass is 86 kg.
a) The teacher catches the first brick. How much kinetic energy did he absorb? How fast is he traveling?
Answer: 97.25 J, 0.227 m/s
b) The teacher deftly blocks the second brick with his forehead, resulting in the brick bouncing back toward the student at 2 m/s. What is his velocity after this collision? Remember he is still holding the first brick!
Answer: 0.5 m/s [away from student]
c) The teacher catches one more brick. What's his velocity?
Answer: 0.71 m/s [away from student]
d) The teacher wants to get away, so he decides to throw bricks back towards the student. He can throw the bricks at 15 m/s (relative to himself). but he can't decide whether it would be better to throw them all at once, or one after the other. Determine which scenario would produce a higher final speed.
Answer: 1.378 m/s vs. 1.385 m/s respectively.
Please help me understand what I'm supposed to do for d). For throwing them all at once I tried:
(90kg)(0.71m/s) = 86vf + (4kg)(15m/s)
(90kg)(0.71m/s) + (4kg)(15ms) = 86vf
(86kg)(0.71m/s) + (4kg)(15ms) = 86vf
...and a million other combinations. Needless to say, none of them have worked and I can't understand momentum. Thanks for any help.
