Question

Driving a fuel-efficient car was never really your way of living, because you believe that anthropogenic climate change is a big hoax. While serving in the Army you learned to truly appreciate the advantages of driving a nice “Humvee” (from High Mobility Multipurpose Wheeled Vehicle = HMMWV). A (highway) gas mileage of 10mpg really does not scare you and you decide to invest in a fully equipped Hummer H1 with a curb weight of mH1 = 3685kg (Note: This is really a “curb mass” and not a “curb weight”=force!). Your neighbor is one of those “environmentalists” who drives a Volkswagen XL1 that he imported into the U.S. It consistently gets a gas mileage of 240mpg and has a curb weight of just mXL1 = 795kg. You really hate that your neighbor can drive from Charleston to Columbia and back for just $2.50 (1gal) while you pay $60.00 (24 times as much) for enjoying your great Hummer during the same drive. Remembering your Physics class you recall that in collisions your Hummer really has an edge. On one of those days when the gas prices soar you had enough and you decide to hit your always smiling neighbor and his car head-on while driving (way too fast) at a speed of vH1 = 60mph. Your neighbor knows, of course, that the speed limit in your residential neighborhood is vXL1 = 25mph to keep children and residents safe.

a) Considering an inelastic collision, what is the final speed of your Hummer with that fuelefficient piece of carbon fiber forever put to rest on top of your hood?

b) Neglecting all mechanical deformations you may also dream of a truly elastic collision. If that was the reality, you and your Hummer could kick your neighbor’s car away like a football. Now assume your neighbor’s car is parked on the street (vXL1 = 0 m s ) and you hit it in an elastic collision with the same speed as before. What are the final velocities of your Hummer and of your neighbor’s car?

Answer 1

a) From conservation of momentum

mH1*vH1+mXL1*vXL1 =( mH1+mXL1) *vHf

Given that mH1= 3685kg

mXL1 = 795kg

vH1= 60mph

vXL1 = -25mph (taking vH1 positive it is moving opposite to vH1 hence it is negative.)

vHf=?

3685*60-795*25 = (3685+795) *VHf

201225 = 4480*vHf

VHf = 201225/4480 = 44.92mph

b) for elastic collision relative velocity of approach = relative velocity of seperation

vH1-0 = vXLf-vHf

vXLf-vHf = 60 mph

vXLf = 60+vHf

From conservation of momentum

3685*60 -0 = 3685*vHf + 795*vXLf

221100= 3685*vHf + 795*60 + 795*vHf

221100 = 4480 *vHf + 47700

4480*vHf = 173400

vHf = 173400/4480= 38.71mph

vXLf = 60+vHf = 60+38.71= 98.71 mph