At the instant shown, cars A and B are traveling at velocities of 50 m/s and 30
ID: 585559 • Letter: A
Question
At the instant shown, cars A and B are traveling at velocities of
50 m/s and 30 m/s , respectively. B is increasing its velocity by 2 m/s2, while A maintains a constant velocity. The radius of curvature at B is ?B = 200 m.
Determine the magnitude of the velocity of B with respect to A.
Determine the direction angle of the velocity of B with respect to A.
Determine the magnitude of the acceleration of B with respect to A.
Determine the direction angle of the acceleration of B with respect to A.
30°Explanation / Answer
Here, Vb/a = Vb - Va
= -30sin30 i + 30cos30 j - 50 j
= - 15 i - 24.019 j m/sec
=> magnitude of the velocity of B with respect to A = sqrt (152 + 24.0192)
= 28.318 m/sec
=> direction angle of the velocity of B with respect to A = 180 + tan-1(24.019/15)
= 238.015 degrees ---anticlockwise from + ve x axis
Here, centripedal acceleration = 30 *30/200
= 4.5 m/sec2
Here, Ab/a = Ab - Aa
= (-2sin30 - 4.5cos30) i + (2cos30 - 4.5sin30) j
= - 4.897 i - 0.5179 j
=> magnitude of the acceleration of B with respect to A = 4.924 m/sec2
=> direction angle of the acceleration of B with respect to A = 180 + tan-1(0.5179/4.897)
= 186.037 degrees ---anticlockwise from + ve x axis
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