### Q.32(a):- Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by

θ(t) = tan^{-1}((v_{0y}– gt) **/** v_{0x})

**Answer:-**

(a) Let v

Let v

_{0x}and v_{0y}respectively be the initial components of the velocity of the projectile along horizontal (*x*) and vertical (*y*) directions.Let v

_{x}and v_{y}respectively be the horizontal and vertical components of velocity at a point P.Time taken by the projectile to reach point P = *t*

Applying the first equation of motion along the vertical and horizontal directions, we get:

v_{y} = v_{0y} = gt

And v_{x} = v_{0x}

∴ tan θ = v_{y} / v_{x} = (v_{0y} – gt) / v_{0x}

θ = tan^{-1} (v_{0y} – gt) / v_{0x}