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The hare and the tortoise are at the starting line together. When the gun goes o

ID: 1976958 • Letter: T

Question

The hare and the tortoise are at the starting
line together. When the gun goes o?, the hare
moves o? at a constant speed of 10 meters per
second. (Ignore the acceleration required to
get the animal to this speed.) The tortoise
starts from a dead stop, but accelerates at a
rate of 2 meters per second per second. Make
a table showing the positions of the two racers
after 1 second, 2 seconds, 3 seconds, and so
forth.
How long will it be before the tortoise
passes the hare?
Answer in units of seconds


In deep space (no gravity), the bolt (arrow)
of a crossbow accelerates at 173 m/s
2
and
attains a speed of 107 m/s when it leaves the
bow.For how long is it accelerated?
Answer in units of s
What speed will the bolt have attained 2.1 s
after leaving the crossbow?
Answer in units of m/s
How far will the bolt have traveled during the
2.1 s?
Answer in units of m

Explanation / Answer

Speed of hare v = 10 m/s Acceleration of tortoise a = 2 m/s2 Then the distance traveled bu each in time for hare x = vt for totoise x = 1/2 at2                                                           t = 1s                                   t = 2s                                       t = 3s                 t = 4s    Hare             10 m                                      20 m                                        30 m                  40 m    Tortoise         1m                                        4 m                                          9 m                     16 m When both passes each other                               vt = 1/2 at2                                v = 1/2 at Therefore the time                                 t = 2v/a                                   = 2 (10 m/s) /2                                   = 10 s ----------------------------------------------------------------------------------------------------------------- (b) Acceleration of crow bar a = 173 m/s2        Final speed v = 107 m/s        From kinematic equations                            v = v0 + at                             107 m/s = 0 + (173 m/s2) t                              t = 107 / 173                                = 0.62 s The speed of the bolt attain after t = 2.1 s                           v = v0 + at                              = 107 m/s + (173 m/s2) (2.1 s)                              = 470.3 m/s The distance travled by crow bar                           x = v0 t +1/2 at2                              = (107 m/s)(2.1s) + (0.5)(173 m/s2) (2.1s) 2                              = 606.165 m                              = 606.165 m