A tortoise can run with a speed of 0.12 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 1.0 minutes. The tortoise wins by a shell (30 cm).

Question

(a) How long does the race take?
(b) What is the length of the race?

Answer 1

(a) Re

Answer 2

Sorry, my computer is acting up.

Answer 3

Write equations for distances travelled vs time for each animal. Assume the hare pauses once, for 60 seconds, during the race.

Set the distance travelled by the tortoise (X1) equal to the distance travelled by the hare (X2) PLUS 0.3 meters.

X1 = 0.12 t meters

X2 = 2.4 (t - 60)

X1 - X2 = 0.12t -2.4t + 144 = 0.3

Solve for t.

143.7 = 2.28 t

t = 63.026 seconds

Using that t, compute X1(t)

X1 = 7.563 m
X2 = 7.263 m

Answer 4

A motor car moving at a speed of 72 km/h can not come to a stop in less than 3 s while for a truck this time interval is 5.0s . On a highway the car is behind the truck both moving at 72 km/h . The truck gives a signal that it is going to stop at emergency. At what distance the car should be from the truck so that it does not bump onto the truck . Human response time is 0.5s