Question
If $${V_1}$$ is velocity of a body projected from the point $$A$$ and $${V_2}$$ is the velocity of a body projected from point $$B$$ which is vertically below the highest point $$C.$$ if both the bodies collide, then
If $${V_1}$$ is velocity of a body projected from the point $$A$$ and $${V_2}$$ is the velocity of a body projected from point $$B$$ which is vertically below the highest point $$C.$$ if both the bodies collide, then
A.
$${V_1} = \frac{1}{2}{V_2}$$
B.
$${V_2} = \frac{1}{2}{V_1}$$
C.
$${V_1} = {V_2}$$
D.
Two bodies can't collide.
Answer :
$${V_2} = \frac{1}{2}{V_1}$$
Solution :
Two bodies will collide at the highest point if both cover the same vertical height in the same time.
$$\eqalign{ & \Rightarrow \frac{{{V_2}}}{{{V_1}}} = \sin {30^ \circ } = \frac{1}{2} \cr & \therefore {V_2} = \frac{1}{2}{V_1} \cr} $$
Two bodies will collide at the highest point if both cover the same vertical height in the same time.
$$\eqalign{ & \Rightarrow \frac{{{V_2}}}{{{V_1}}} = \sin {30^ \circ } = \frac{1}{2} \cr & \therefore {V_2} = \frac{1}{2}{V_1} \cr} $$
