Physics MOTION... Help please...?

Question

1) A police car leave sin pursuit of a hold up car 0.50 h after the latter has left the crime at 75 mi/h. How fast must the police go if it is to catch up with the hold up car in 1h?

2) A snake is slithering toward you at 1.5 m/s. If you start walking when it is 5m away, how fast must you go in order that the snake not overtakes you when you had gone 40 m?

3) A hare and a tortoise compete in a race over a course 1.0 km long. The tortoise crawls straight and steadily at its maximum speed of 0.2 m/s toward the finish line. The hare runs at its maximum speed of 8.0 m/s toward the goal for 0.8 km and then stops to tease the tortoise. How close to the goal can the hare let the tortoise approach before resuming the race, which the tortoise wins in a photo finish? Assume that, when moving, both animals move steadily at their respective maximum speeds.

Thanks to those who'll be helping me.. I really don't know how to solve these physics problems..

Answer 1

1) After 1/2 hr, the criminal's car would be 37.5 miles away.

Let Vp/c be the velocity of the police car with respect to the velocity of the criminal's car.

Vp/c = 37.5 miles/h
Vp/c = Vp - Vc
37.5mi/h = Vp - 75mi/h
Vp = 112.5mi/h (Ans)

2) To reach your 40m mark, the snake would have to cover 45m.

Hence it will take 45/1.5 = 30s for the snake to catch up with you at the 40m mark.

Within 30s, you will have to travel 40m. Hence, your speed will be 40/30 m/s = approx 1.33 m/s. (Ans)

3) If the hare stops at the 0.8km mark, that means that there'll be 200m more left to go.

The hare will take 200/8 = 25 seconds to finish the last 200m of the race.

For a draw, the tortoise would also have to complete the race within the 25 seconds.

25s * 0.2m/s = 5m
For a draw, the hare must let the tortoise approach 5m away from the goal.

Hence, for the tortoise to win, it has to get closer than 5m away from the goal. =)

Answer 2

1. to catch up they must go the same distance and this is to be at time = 1 hour after the police start.

hold up car: d1 = (t + .5)75 = 1.5*75 = 112.5
police car: d2 = tv = v

v = 112.5 m/h

2. the snake must cover a distance of 45 m at 1.5 m/s. He does this in t = 30 seconds

you must move 40 m in 30 seconds so v = 40/30 m/s
Your speed must be 1 and 1/3 m/s

3.The hare has .2 km or 200 m to go. since he can run at 8 m/s it would take him a time of 200/8 seconds or 25 seconds. So it would take the hare 25 seconds to reach the finish line from the point where he stopped.

The tortoise in 25 seconds can move .2*25 or 5 meters.
So the tortoise can get to within 5 meters of the finish line and the hare can still win in a photo finish.