September 5, 2007
PHY2053
Quiz 1
Chapter 2
Name:
UFID:
1. (5 pts) A car travels at 30 mi/h for 40 minutes and then 40 mi/h for 45 minutes. How
much distance the car travels in total?
40min=40min×(1h/60min)=2/3h
45min=45min×(1hr/60min)=3/4h
The total distance=30mi/h×2/3h+40mi/h×3/4h=20+30=50mile
2. (5 pts) Suppose you leave your house 10 minutes before the class starts and head for
the university by bike. The university is 2.8 km away from your house. You run 1.2 km
at a constant speed and then the bike chain comes off. It takes 1 minute and 40 seconds
to fix the chain. After you fix the chain, you run twice as fast. You get to the class just on
time. What is the speed of the bike (in m/s) before fixing the chain?
The total time you are on the bike=600s-100s=500s
Express this in terms of the unknown and solve the equation:
500=1200/v+1600/2v
v=4m/s
3. (5 pts) A balloon moving straight up with speed 24.0 m/s releases a ball at a height of
120 m above the ground. Find the time needed for the ball to reach the ground.
Plug the values in y=v₀t-(1/2)gt².(The initial velocity is 24.0m/s.)
-120=24t-(1/2)×9.8t²
t={24+√(24²+4×4.9×120)}/(2×4.9)=7.97s
4. (5 pts) A ball is dropped from the top of the building, at an initial height of 180.0m
above the ground. Two seconds later, another ball is thrown downward so that it hits the
first ball before the first ball reaches the ground. What is the minimum initial speed of
the second ball? (You can use g = 10 m/s² for this problem.)
The time the first ball reaches the ground:
-180=-(1/2)10t², t²=36, t=6s
If the second ball reaches the ground within 4 second after you throw it, it hits the first
ball. Thus,
-180=v₀×4-(1/2)×10×4², v₀=-25m/s
The minimum speed=25m/s (Speed is the magnitude of velocity)