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1). A motorist is traveling at 18.2 m/s when he sees a deer in the road 38.1 m ahead.

(a) If the maximum negative acceleration of the vehicle is -4.50 m/s2, what is the maximum reaction time t of the motorist that will allow him to avoid hitting the deer?
s
(b) If his reaction time is actually 0.300 s, how fast will he be traveling when he hits the deer?
m/s

2)An inquisitive physics student and mountain climber climbs a 50.0 m cliff that overhangs a calm pool of water. He throws two stones vertically downward, 1.00 s apart, and observes that they cause a single splash. The first stone has an initial speed of 2.00 m/s.
(a) How long after release of the first stone do the two stones hit the water?
s
(b) What was the initial velocity of the second stone?
m/s (downward)
(c) What is the velocity of each stone at the instant the two hit the water?
first stone
m/s (downward)
second stone
m/s (downward)

2007-09-03 16:10:27 · 1 answers · asked by justin l 1 in Science & Mathematics Physics

1 answers

1. The car will stop according to
d(t)=18.2*t-.5*4.50*t^2

v(t)=18.2-4.5*t

And v(t) when stopped =0
0=18.2-4.5*t
so the stopping time is
18.2/4.5
4.044 seconds
stopping distance is
d(4.044)=18.2*4.044-.5*4.5*4.044^2
36.8 m
that is a margin of 1.3 m

If the reaction time is 0.300 seconds
then the car has traveled
18.2*0.300 meter or
5.46 meters, so the separation is now
32.64 meters

to find the speed at impact, find the time to impact as
32.64=18.2*t-.5*4.5*t^2
solve for t
2.68 seconds
v(2.68)=18.2-4.5*2.68
6.14 m/s

if the two stones strike the water simultaneously, then the following equations must be true:

50=2*t+.5*9.81*t^2
50=v2*(t-1)+.5*9.81*(t-1)^2

solve for t from the first equation
t=3 seconds (use the positive root, the negative root describes the scenario where the stone was fired upward from the water and fell back passing the edge of the cliff at 2 m/s)

now that we have t, solve the second equation for v2:
50=v2*2+.5*9.81*4
v2=15.9 m/s

to get velocity at impact
for stone #1:
v1=2+9.81*3
v1=31.43 m/s

stone #2
v2=15.9+9.81*2
v2=35.52 m/s

j

2007-09-04 12:22:42 · answer #1 · answered by odu83 7 · 1 0

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