Question

Two particles A,and B are projected from the same point on the ground .Particle A is projected on a smooth horizontal surface with speed v, where as B is projected into air with speed 2v/root3. The two particles collide when the particle B drops on the surface for the first time.

1. the angle with which particle B was projected into air is 37 degree
2. sepration between the two particles when B is at highest position is v^m/2g
3. the angle with which particle was projected into air is 30 degree
4. sepration between the two particles when B is at highest position is v^2m/6g

Answer 1

Dear Student,
$$\begin{gathered} lettotaltimeisTthenandangleofprojectionofBis\theta \\ thenaccordingtoquestion \\ RangevT=\frac{4v^2\sin \left(2\theta \right)}{3g}----1 \\ andT=\frac{4v\sin \left(\theta \right)}{\sqrt{3}}----2 \\ putthevalueofTfrom2to1weget \\ \cos \left(\theta \right)=\frac{\sqrt{3}}{2} \\ \theta =30 \\ andforseperation \\ maximumheightisseperation=\frac{4v^2{\sin }^2\left(\theta \right)}{3\times 2g}=\frac{v^2}{6g} \end{gathered}$$
Regard