Question
A particle is projected at an angle of elevation $$\alpha $$ and after $$t$$ seconds it appears to have an angle of elevation $$\beta $$ as seen from point of projection. The initial velocity will be
A.
$$\frac{{gt}}{{2\sin \left( {\alpha - \beta } \right)}}$$
B.
$$\frac{{gt\cos \beta }}{{2\sin \left( {\alpha - \beta } \right)}}$$
C.
$$\frac{{\sin \left( {\alpha - \beta } \right)}}{{2gt}}$$
D.
$$\frac{{2\sin \left( {\alpha - \beta } \right)}}{{gt\cos \beta }}$$
Answer :
$$\frac{{gt\cos \beta }}{{2\sin \left( {\alpha - \beta } \right)}}$$
Solution :
$$t = \frac{{2u\sin \left( {\alpha - \beta } \right)}}{{g\cos \beta }};\,u = \frac{{gt\cos \beta }}{{2\sin \left( {\alpha - \beta } \right)}}$$