Two motorcars, A and B are appraching each other . At time t=0 car A and B are at 975m. With their speeds being 30m/s2 and 17m/s2 respectively and car A passed point b for 40s and car B passes at 42s. What is the speed of car B relative to car A when they pass each other
To find the speed of car B relative to car A when they pass each other, we need to find the speeds of both cars at the point of passing.
Given:
Initial distance between car A and car B, d = 975 m
Speed of car A, v_A = 30 m/s^2
Speed of car B, v_B = 17 m/s^2
Time taken by car A to pass point B, t_A = 40 s
Time taken by car B to pass point B, t_B = 42 s
Let's first find the distances covered by car A and car B in the given time intervals.
Distance covered by car A, s_A = v_A * t_A
Distance covered by car B, s_B = v_B * t_B
Since car A starts passing point B two seconds before car B, the distance covered by car A at the point of passing is equal to s_A + 2 * v_A. This can be calculated as:
Distance covered by car A at point of passing = s_A + 2 * v_A = (v_A * t_A) + 2 * v_A
Similarly, the distance covered by car B at the point of passing is s_B + v_B. This can be calculated as:
Distance covered by car B at point of passing = s_B + v_B = (v_B * t_B) + v_B
Since the initial distance between car A and car B is 975 m, the relative distance between them at the point of passing can be calculated as:
Relative distance at point of passing = Initial distance - (Distance covered by car A at point of passing + Distance covered by car B at point of passing)
Relative distance at point of passing = 975 - [(v_A * t_A) + 2 * v_A + (v_B * t_B) + v_B]
Finally, to find the speed of car B relative to car A, we divide the relative distance at the point of passing by the time difference between car A and car B passing point B:
Speed of car B relative to car A = Relative distance at point of passing / (t_B - t_A)
Plug in the given values to calculate the speed of car B relative to car A.