Question

A man A is sitting in a car at rest observes a man B on bike moving away from him with velocity $16m{s}^{-1}$, a man C walking on road with velocity $2m{s}^{-1}$, towards him and a bird flying with speed $20m{s}^{-1}$ at angle ${37}^o$ with horizontal as shown in Fig. Find the
a. velocity of car, bird, and man C as seen by man B.
b. velocity of car, bird and man B as seen by man C.
c. velocity of car, than B, and man C as seen by bird:

Answer 1

Given; ${\overrightarrow{v}}_B=16\hat{i}m{s}^{-1}$, ${\overrightarrow{v}}_C=-2\hat{i}m{s}^{-1}$

${\overrightarrow{v}}_{bird}=(20cos{37}^o\hat{i}+20sin{37}^o\hat{j})m{s}^{-1}=16\hat{i}+12\hat{j}m{s}^{-1}$

a. Observation from man B:

i. ${\overrightarrow{v}}_{car,B}={\overrightarrow{v}}_{car}-\overrightarrow{v}B=0-16\hat{i}=-16\hat{i}m{s}^{-1}(\leftarrow )$

ii. ${\overrightarrow{v}}_{bird,B}={\overrightarrow{v}}_{bird}-{\overrightarrow{v}}_B=(16\hat{i}+12\hat{j})-16\hat{i}=12\hat{j}m{s}^{-1}(\uparrow )$

iii. ${\overrightarrow{v}}_{C,B}={\overrightarrow{v}}_C-{\overrightarrow{v}}_B=(-2\hat{i})-\left(16\hat{i}\right)=-18\hat{i}m{s}^{-1}(\leftarrow )$

b. Observation from man C:

i. ${\overrightarrow{v}}_{car,C}={\overrightarrow{v}}_{car}-{\overrightarrow{v}}_C{\overrightarrow{v}}_C=0-(-2\hat{i})=2\hat{i}m{s}^{-1}(\to )$

ii. ${\overrightarrow{v}}_{bird,C}={\overrightarrow{v}}_{bird}-{\overrightarrow{v}}_C=(16\hat{i}+12\hat{j})-(-2\hat{i})=18\hat{i}+12\hat{j}m{s}^{-1}(\nearrow )$

iii. ${\overrightarrow{v}}_{B,C}={\overrightarrow{v}}_B-{\overrightarrow{v}}_C=16\hat{i}-(-2\hat{i})=18\hat{i}m{s}^{-1}(\to )$

c. Observation from bird:

i. ${\overrightarrow{v}}_{car,bird}={\overrightarrow{v}}_{car}-{\overrightarrow{v}}_{bird}=0-(16\hat{i}+12\hat{j})=-16\hat{i}-12\hat{j}m{s}^{-1}(\swarrow )$

ii. ${\overrightarrow{v}}_{B,bird}={\overrightarrow{v}}_B-{\overrightarrow{v}}_{bird}=16\hat{i}-(16\hat{i}+12\hat{j})=-12\hat{i}m{s}^{-1}(\downarrow )$

iii. ${\overrightarrow{v}}_{C,bird}={\overrightarrow{v}}_C-{\overrightarrow{v}}_{bird}=(-2\hat{i})-(16\hat{i}+12\hat{j})=-18\hat{i}-12\hat{j}m{s}^{-1}(\swarrow )$