Question Number 47194 by Necxx last updated on 06/Nov/18
$${The}\:{velocity}\:{of}\:{a}\:{ship}\:{Q}\:{relqtive}\:{to} \\ $$$${a}\:{ship}\:{P}\:\:{is}\:\mathrm{10}{km}/{h}\:{in}\:{a}\:{direction} \\ $$$${N}\mathrm{45}^{.} {E}.{If}\:{the}\:{velocity}\:{of}\:{P}\:\:{is}\:\mathrm{20}{km}/{h} \\ $$$${in}\:{a}\:{direction}\:{N}\mathrm{60}^{.} {W}.{Find}\:{the} \\ $$$${actual}\:{velocity}\:{of}\:{Q}\:{in}\:{magnitude} \\ $$$${and}\:{direction}. \\ $$
Commented by Necxx last updated on 06/Nov/18
$${please}\:{help} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 06/Nov/18
Commented by tanmay.chaudhury50@gmail.com last updated on 06/Nov/18
Commented by tanmay.chaudhury50@gmail.com last updated on 06/Nov/18
$${picture}\:{for}\:{clarity}\:{of}\:{direction}… \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 06/Nov/18
$$\overset{\rightarrow} {{V}}_{{p}} =−\mathrm{20}{sin}\mathrm{60}^{{o}} {i}+\mathrm{20}{cos}\mathrm{60}^{{o}} {j} \\ $$$${velocity}\:{of}\:{Q}\:{relative}\:{to}\:{P}\:{is} \\ $$$$\overset{\rightarrow} {{V}}_{{Q}} −\overset{\rightarrow} {{V}}_{{P}} =\mathrm{10}{sin}\mathrm{45}^{{o}} {i}+\mathrm{10}{cos}\mathrm{45}^{{o}} {j} \\ $$$$\overset{\rightarrow} {{V}}_{{Q}} ={i}\left(\mathrm{10}×\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\mathrm{20}×\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)+{j}\left(\mathrm{10}×\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\mathrm{20}×\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$\overset{\rightarrow} {{V}}_{{Q}} ={i}\left(\mathrm{5}×\mathrm{1}.\mathrm{41}−\mathrm{10}×\mathrm{1}.\mathrm{732}\right)+{j}\left(\mathrm{5}×\mathrm{1}.\mathrm{41}+\mathrm{10}\right) \\ $$$$\:\:={i}\left(\mathrm{7}.\mathrm{05}−\mathrm{17}.\mathrm{32}\right)+{j}\left(\mathrm{7}.\mathrm{05}+\mathrm{10}\right) \\ $$$$={i}\left(−\mathrm{10}.\mathrm{27}\right)+{j}\left(\mathrm{17}.\mathrm{5}\right) \\ $$$${pls}\:{check}… \\ $$
Commented by Necxx last updated on 06/Nov/18
$${yeah}….\:{i}\:{cqlculated}\:{the}\:{modulus} \\ $$$${and}\:{direction}\:{of}\:{the}\:{value}.{its}\:{really} \\ $$$${correct}.{Thanks} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 06/Nov/18
$${thanks}\:… \\ $$