at a given instant two cars are at distances 300 and 400m from the point of intersection O oftwo straight roads crossing at a right angle and are approaching O at uniform speeds of 20 and 40m/s respectively. find the shortest distance between the cars and the time taken to reach this position
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To find the shortest distance between the two cars, let's first analyze the situation.
We have two cars approaching the intersection O from different directions on straight roads. The car distances from O are 300m and 400m, and their speeds are 20m/s and 40m/s, respectively.
Let's assume car A is closer to O (300m) and car B is farther away (400m). As the cars approach O, they will eventually cross paths at some point.
To find the time taken for this to happen, we can use the equation:
time = distance / speed
For car A:
time = 300m / 20m/s = 15 seconds
For car B:
time = 400m / 40m/s = 10 seconds
Since car B takes 10 seconds to reach O after car A, this means that car B will be at O when car A has already traveled some distance beyond it.
The distance traveled by car A in 10 seconds is:
distance = speed * time = 20m/s * 10s = 200m
Now, let's calculate the shortest distance between the two cars. This can be done by considering the difference in distances traveled by both cars.
Shortest distance = distance traveled by car B - distance traveled by car A
= 400m - 200m
= 200m
Therefore, the shortest distance between the two cars is 200 meters.
To find the time taken to reach this shortest distance, we look at the time when both cars are at this distance from O, which is 200m.
For car A:
time = distance / speed = 200m / 20m/s = 10 seconds
So it will take 10 seconds for car A to reach the shortest distance from O. Since car B is already at this distance, the time taken for car B is 0 seconds.
In conclusion, the shortest distance between the two cars is 200 meters, and it will take car A 10 seconds to reach this position.