22. A professor holds a $1,000,000 bill above the hand of a student who is poise

Question

22. A professor holds a $1,000,000 bill above the hand of a student who is poised to catch the bill as it falls between his fingers. After the release is made, the student catches the bill when it has fallen 11 cm. For how long was the bill falling? [For this problem assume the existence of $1,000,000 bills.]

23. Joe Newton can bring his fully loaded 18-wheel Mac truck smoothly from 25 m/s to a complete stop in a distance of 97 meters. What would Joe’s stopping distance be in meters if his starting speed were 30 m/s? You may pretend that Joe’s reaction time is negligible for this problem and that his (steady) deceleration is the same in both cases.

24.A fisherman must row directly across a river of width D to get back to his camp. In still water, he can row with speed vf (‘f’ for fisherman), but the river is moving with speed vr (‘r’ for river). How long will it take him to cross the river? You may assume he travels straight across the river to the other side.

Explanation / Answer

22. The bill was initially at rest. The initial velocity u = 0
We need to find the time t taken by the bill to fall a distance of d = 11 cm
Using Newton's equations of motion
d = u t + (1/2) a t2
d = (1/2) g t2
t = sqrt(2 d / g)
t = sqrt (2 x 0.11 m / 9.81 m/s2)
t = 0.1497 s
This is the time taken by the bill to fall 11 cm

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