A bridge that was 10.4 m long has been washed out by the rain several days ago.How fast must a car be going to successfully jump the stream,if we neglect air resistance? Although the road is level on both sides of the bridge,the road on the far side is 3.00 m lower than the road on this side.
A)18.8 m/s
B)13.3 m/s
C)10.9 m/s
D)26.6 m/s
E)14.3 m/s

Question

Quizplus · Accepted Answer

Using conservation of energy:
initial kinetic energy = final potential energy + final kinetic energy
1/2 mv^2 = mgh + 1/2 mvf^2
vf^2 = v^2 - 2gh
vf = sqrt(v^2 - 2gh)
vf = sqrt((2g)(10.4 + 3))
vf = sqrt(26g)
vf = 16.08 m/s
Therefore, the car must be going at least 16.08 m/s to make it across the stream. The only answer choice close to this value is B) 13.3 m/s.

A Bridge That Was 10