Two cars, A and B, travel in the same direction on a straight section of highway. A has a speed of 69.5 km/h, and B a speed of 84.3 km/h (both relative to the earth).
(b) If A is initially 394 m in front of B, how long will it take for B to reach A?
To find the time it takes for car B to reach car A, we need to determine the relative speed between the two cars.
The relative speed between car A and car B can be calculated by subtracting the speed of car A from the speed of car B:
Relative speed = Speed of car B - Speed of car A
Relative speed = 84.3 km/h - 69.5 km/h
Relative speed = 14.8 km/h
Now, we need to convert the relative speed to meters per second (m/s) because the initial distance between the two cars is given in meters.
To convert km/h to m/s, we divide the speed in km/h by 3.6:
Relative speed in m/s = (Relative speed in km/h) / 3.6
Relative speed in m/s = 14.8 km/h / 3.6
Relative speed in m/s ≈ 4.11 m/s
We can now use the formula: time = distance / speed to find the time it takes for car B to reach car A.
The distance that car B needs to cover to reach car A is 394 meters.
Time = Distance / Relative speed
Time = 394 m / 4.11 m/s
Time ≈ 95.84 seconds
Therefore, it will take approximately 95.84 seconds for car B to reach car A.
Da = 69.5*T
Db = 84.3*T
B will have to travel 394 m(0.394km) farther than A to catch up:
Db = Da + 0.394km
84.3 * T = 69.5 * T + 0.394
84.3T-69.5T = 0.394
14.8T = 0.394
T = 0.02662 h. = 1.60 Min. to catch up.