Two birds are flying horizontally at the same elevation but

Two birds are flying horizontally at the same elevation but have different velocities and accelerations as indicated on the diagram. Bird A is flying along a circular path (r =10 ft) and Bird B is flying on a straight path. All velocities and accelerations given are only the tangent terms for their respective paths.What is the acceleration of bird A with respect to Bird B?

Solution

centripetal acceleration of bird A

aAc = vA^2/r = 8^2/10 = 6.4 ft/s2

tangential acceleration of A

aAt = 10 ft/s2

So, total accelration, aA = -6.4 i - 10 j <----- using vector notation

aB = -32.2 j ft/s2

So, acceleration of A with respect to B

aAB = aA - aB = -6.4 i + (32.2 -10 ) j

= -6.4 i + 22.2 j

So, magnitude of relative acceleration = sqrt(6.4^2+22.2^2) = 23.1 ft/s2 <-------answer