Boat A is traveling due south along a straight path with a s

Boat A is traveling due south along a straight path with a speed of vA and acceleration aA. Boat B is traveling along a circular path of radius R with a constant speed of vB. At the instant shown, B is traveling due east.

Find: For this instant: a) Determine the velocity and acceleration of boat B as seen by the driver of boat A. Write your answers as vectors.

b) What is the speed and rate of change of speed of B as observed by the driver of boat A? Also, what is radius of curvature of the path of B as observed by the driver of boat A?

Use the following parameters in your analysis: R = 150 m, vA = 30 m/s, aA = 3 m/s2 and vB = 20 m/s

Solution

a)

velocity of A with respect to ground,

vA = -vA j <---------- j is the unit vector along y axis

acceleration of A with respect to ground,

aA = -3 j m/s2

velocity of B with respect to ground,

vB = vB i

acceleration of B with repect to ground, aB = vB^2/R k

So, velocity of B with respect to A:

vBA = vB - vA

= vBi - (-vA j)

= vB i + vA j

=( 20 i + 30 j ) m/s <--------answer

acceleration of B with repect to A,

aBA = aB - aA

= vB^2/R k - (-3 j)

= 20^2/150 k + 3j

= 2.67 k + 3 j <------answer

b)

speed of B with repect to A,

| vBA | = sqrt(vA^2 + vB^2)

= sqrt(30^2+20^2)

= 36.1 m/s2 <------answer

rate of change of speed = sqrt(2.67^2 +3^2)

= 4.02 m/s2<-------answer