How fast would a 9-g fly have to be traveling to slow a 1790-kg car traveling at 58 mph by 4 mph if the fly hit the car in a totally inelastic head-on collision?

Answer 1

Then the car's initial velocity is -50 mph.
The collision is totally inelastic, so the final velocity of both fly and car is -44 mph.

Total initial momentum = (4/1000)u - 1980*50 = 0.004u - 99000 kg mph.
Total final momentum = (1980 + 4/1000)*(-44) = -87120.176 kg mph.

Momentum is conserved, so 0.004u - 99000 = -87120.176.
�ˆ 0.004u = 99000 - 87120.176 = 11879.824.
�ˆ u = 11879.824/0.004 = 2969956 mph.

So the fly's velocity would have to be 2,969,956 mph. That's almost 825 miles per second!
Just plug in your numbers and chug away.

Answer 2

How are you getting -44 mph for the final velocity?