Question

Two bodies are projected horizontally from the top of a tower of height H in opposite directions with velocities u₁ and u₂ then the time after which the velocity vectors for making an angle theta with each other.

Answer 1

\(\vec {V_y} = 0 - gt(j)\)

\(\vec {V_y} = -gt\hat j\)

\(\vec {V_A} = u_1 \hat i - gt\hat j\)

\(\vec {V_B} =- u_1 \hat i - gt\hat j\)

For perpendicular \( \vec {V_A}.\vec {V_B} = 0\) 

\((u_1 \hat i - gt\hat j) (- u \hat i - gt\hat j)=0\)

\(- u_1 u_2 + g^2 t^2 = 0\)

\(t = \frac{\sqrt{u_1u_2}}g\)