a car is moving with a constant speed of 40 km/h along a straight road which heads towards a large vertical wall and makes a sharp 90 degree turn by the side of the wall.a fly flying at a constant speed of 100km/h,starts from the wall towards the car at an instant when the car is 20 km away ,flies until it reaches the glass pane of the car and returns to the wall at the same speed.it continues to fly b/w the car and the wall till the car makes the 90 degree turn.
a)what is the total distance the fly has traveled during this period ?
b)how many trips has it made b/w the car and wall??????

To tackle this problem, we need to analyze the motion of both the car and the fly. The car is moving towards the wall at a constant speed, while the fly is flying back and forth between the wall and the car. Let's break this down step by step.

Understanding the Car's Journey

The car is traveling at a speed of 40 km/h and starts 20 km away from the wall. To find out how long it takes for the car to reach the wall, we can use the formula:

• Time = Distance / Speed

Substituting the values:

• Time = 20 km / 40 km/h = 0.5 hours (or 30 minutes)

The Fly's Flight Time

During the time the car is approaching the wall, the fly is continuously flying back and forth. The fly's speed is 100 km/h. Since the car takes 0.5 hours to reach the wall, we can determine how far the fly travels in that time:

• Distance = Speed × Time

Calculating the distance:

• Distance = 100 km/h × 0.5 hours = 50 km

Calculating the Number of Trips

Next, we need to find out how many trips the fly makes between the wall and the car. To do this, we first need to determine the distance between the wall and the car at the start, which is 20 km. The fly travels to the car and back to the wall, covering a total distance of 40 km for each round trip.

Now, we can find out how many complete trips the fly can make in the time it takes for the car to reach the wall:

• Number of Trips = Total Distance Traveled by Fly / Distance per Trip

Substituting the values:

• Number of Trips = 50 km / 40 km = 1.25 trips

Since the fly can only complete whole trips, it makes 1 complete trip to the car and back to the wall, and then it starts its second trip towards the car but doesn't complete it before the car turns.

Final Summary

In summary:

• The total distance the fly has traveled during the time the car reaches the wall is 50 km.
• The number of complete trips the fly has made between the wall and the car is 1 trip.

This problem illustrates the fascinating dynamics of relative motion and how different speeds can lead to interesting outcomes in scenarios involving moving objects.