You are driving at a constant speed v0 on a straight highway that passes under a

ID: 2272550 • Letter: Y

Question

You are driving at a constant speed v0 on a straight highway that passes under an overpass. At time t=0 , when

your car is a distance from the overpass, a prankster on the overpass releases a water balloon from rest from

a height h above the highway below.

Answer the following questions. You should treat the car as a point particle, ignoring its height, length, and width.

(a) Suppose that you dont see the water balloon until it explodes on your windshield. At what speed

were you v0 originally traveling, given that the water balloon strikes your car? Express your answer in terms of d,h , and any

relevant constants. Simplify your answer as much as possible.

(b) Now suppose that you see the prankster release the water balloon at t=0 , and you slam on your brakes at

time tb in an attempt to avoid being hit. (Your reaction time is tb bigger than 0 .) Your car slows down with a constant

acceleration of magnitude aS . The balloon hits the highway right in front of your car at the instant your car comes

to rest. At what speed v0 were you originally traveling, given that the water balloon just barely misses your car?

Express your answer in terms of ,d ,h

,aS ,tB and any relevant constants. Simplify your answer as much as possible.

speeds is larger? Justify your answer mathematically, with comments as necessary.

d^2/V0^2 = 2h/g

hence Va = d*(sqrt(g/2h))

tB + Vb/aS = sqrt(2h/g)

hence Vb = (sqrt(2h/g)-tB)*aS m/s

since the car is deaccelerating to rest in the sane time as of first case hence

speed of car in second case is higher than speed in first case

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