A body is projected at t=0 with a velocity 10 ~ms ⁻¹ at an angle of 60^ with the horizontal. The radius of curvature of its trajectory at t=1 s is R . Neglecting air resistance and taking acceleration due to gravity g=10 ~ms ⁻² , the value of R is :

Step-by-step solution

Given Data: Initial velocity, u=10 ~m / s Angle of projection, =60^ Radius of curvature at t=1 s is R Acceleration due to gravity, g=10 ~m / s Finding the radius of curvature: Resolving the velocity into x and y components, at any time t aligned & v_x=u 60^ =10 1 2 & v_x=5 ~m / s & v_y=u 60^ +a t= 10 3 2 -10 t & v_y=|5 3 -10 t| aligned At t=1 s v_y=|5 3 -10| Angle made by body with respect to horizontal axis at t=1 ~s aligned & = | v_y v_x |= | 5 3 -10 5 |, & ==| 3 -2| & = ⁻¹(| 3 -2|)=15^ aligned The radius of curv