Answer each of the following questions independently.Two cars C1 and C2 start their journey from two different points at 4 kmph and 3 kmph respectively and meet after 5 hours at a point where their paths make an angle of 135°. After the cars met, they interchange their paths. Each car first travels to the other car's starting point (i.e. C1 travels to C2's starting point along the path C2 was travelling on and C2 travels to C1's starting point along the path C1 was travelling on ) and then travels along the straight line path (i.e. the shortest distance) joining the starting points of the two cars, finally reaching it's original starting point. Find the approximate time interval between the return of C1 and C2 to their starting positions.
Question
Answer each of the following questions independently.Two cars C1 and C2 start their journey from two different points at 4 kmph and 3 kmph respectively and meet after 5 hours at a point where their paths make an angle of 135°. After the cars met, they interchange their paths. Each car first travels to the other car's starting point (i.e. C1 travels to C2's starting point along the path C2 was travelling on and C2 travels to C1's starting point along the path C1 was travelling on ) and then travels along the straight line path (i.e. the shortest distance) joining the starting points of the two cars, finally reaching it's original starting point. Find the approximate time interval between the return of C1 and C2 to their starting positions.
Solution
The problem can be solved in the following steps:
Step 1: Calculate the distance each car traveled before they met. Since they met after 5 hours, the distance traveled by C1 is 4 kmph * 5 hours = 20 km and the distance traveled by C2 is 3 kmph * 5 hours = 15 km.
Step 2: Calculate the distance between the starting points of the two cars. Since the paths make an angle of 135°, we can use the law of cosines to find the distance between the starting points. The law of cosines states that c² = a² + b² - 2abcosC, where a and b are the sides of a triangle and C is the angle between them. In this case, a = 20 km, b = 15 km, and C = 135°. So, c² = 20² + 15² - 22015*cos
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