A man `A` is sitting in a car at rest observes a man `B` on bike moving away from him with velocity `16 m s^-1`, a man `C` walking on road with velocity `2 ms^-1` towards him and a bird flying with spedd `20 ms^-1` at angle `37^@` with horizontal as shown in (Fig. 5.74). Find the
(a) velocity of car, bird, and man `C` as seen by man `B`.
(b) velocity of car, bird, man `B` as seen by man `C`
( c) velocity of car, man `B`, and man `C` as seen by bird.
.

Explanation

Given , `vec v_B = 16 hat i ms^-1, vec v_C = -2 hat i ms^-1`
`vec v_(bird) = (20 cos 37^@ hat i + 20 sin 37^@ hat j) m s^-1 = 16 hat i + 12 hat j m s^-1`
(a) Observation from man B :
(i) `vec v_(car,B) = vec v_(car) - vec vB = 0 - 16 hat i = - 16 hat i ms^-1 (larr)`
(ii) `vec v_(bird,B) = vec v_(bird) - vec v_B = (16 hat i+ 12 j) - 16 hat i= 12 aht j m s^-1 (uarr)`
(iii) `vec v_(C,B) = vev v_C - vec v_B = (-2 hat i) - (16 hat i) = -18 hat i m s^-1 (larr)`
(b) Observation from man `C`
(i) `vec v_(car, C) = vec v_(car) - vec v_C v_C = 0 - (-2 hat i) = 2 hat i ms^-1 (rarr)`
(ii) `vec v_(bird, C) = vec v_(bird) - vec v_C = (16 hat i + 12 hat j) - (-2 hat i)`
=`18 hat i + 12 hat j m s^-1 (rarr)`
(iii) `vec v_(B,C) = vec v_B - vec v_C = 16 hat i -(-2 hat i) = 18 hat i m s^-1 (rarr)`
( c) Observation from bird
(i) `vec v_(car, bird) = vec v_(car) = -vec v_(bird) = 0 - (16 hat i + 12 hat j)`
=`- 16 hat i - 12 hat j m s^-1 (darr)`
(ii) `vec v_B, bird = vec v_B -m vec v_(bird) = 16 hat i - (16 hat i + 12 hat j) = -12 hat i m s^-1 (darr)`
(iii) `vec v_(C, bird) = vec v_C - vec v_(bird) = (-2 hat i) - (16 hat i + 12 hat j)`
=`-18 hat i - 12 hat j m s^-1 (darr)`.