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).

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

(a) Re

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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

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

To find the answers to these questions, we can break down the problem into several steps:

Step 1: Determine the hare's speed.
Given that the tortoise's speed is 0.12 m/s and the hare is 20 times faster, we can calculate the hare's speed as follows:
Hare's speed = 20 * tortoise's speed
Hare's speed = 20 * 0.12 m/s = 2.4 m/s

Step 2: Calculate how long it takes for the hare to rest.
The hare stops to rest for 1.0 minute, which we need to convert into seconds. Since 1 minute is equal to 60 seconds, the time the hare rests is:
Resting time = 1.0 minute = 1.0 * 60 seconds = 60 seconds

Step 3: Determine the distance the tortoise travels during the hare's rest.
The tortoise's lead is given as 30 cm. We need to convert it to meters before we can use it in the calculation:
Tortoise's lead = 30 cm = 30/100 m = 0.3 m

Step 4: Calculate the time it takes for the hare to catch up to the tortoise.
To calculate this, we need to find out how much the hare gains on the tortoise every second. The difference in their speeds is:
Speed difference = hare's speed - tortoise's speed
Speed difference = 2.4 m/s - 0.12 m/s = 2.28 m/s

The time it takes for the hare to catch up to the tortoise is then determined by dividing the distance the tortoise is ahead by the speed difference:
Time to catch up = Tortoise's lead / Speed difference
Time to catch up = 0.3 m / 2.28 m/s

Now we can calculate the answers to the questions:

(a) How long does the race take?
The race will take the total time it takes for the hare to catch up to the tortoise, plus the resting time of the hare:
Race time = Time to catch up + Resting time
Race time = 0.3 m / 2.28 m/s + 60 seconds

(b) What is the length of the race?
The length of the race is simply the distance the hare travels while catching up to the tortoise. Since the tortoise's lead is 0.3 m and the hare catches up to the tortoise, the length of the race is equal to the tortoise's lead:
Length of the race = 0.3 m

By plugging in the values from the calculations, you can find the specific answers to these questions.