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((v0y- gt) / v0x) | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-4 Motion In A Plane



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((v0y– gt) / v0x)

 

Answer:-

(a) Let v0x and v0y respectively be the initial components of the velocity of the projectile along horizontal (x) and vertical (y) directions.
Let vx and vy 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:
vy = v0y = gt
And vx = v0x
∴ tan θ = vy / vx = (v0y – gt) / v0x
θ = tan-1 (v0y – gt) / v0x