Answer to Question #259342 in Mechanics | Relativity for Farjana Akter

Question

Say mr karim runs on a plain land and jumps from a spot in forward direction. Recognize and describe his jumping motion through an equation and make an argument for your answer.

Answer 1

Motion of Mr Karim is projectile motion, whose equation is obtained as follows. Let his initial velocity just before jump be v₀ and angle by θ. Thus his initial velocity has two components:

horizontal or x-component $=v_0 cos θ$

vertical or y-component $= v_0 sin θ$

Let (x,y) be his position at any time t, thus

$x = v_0 cos θ t \\ t = \frac{x}{v_0 cos θ} \\ y = v_0 sin θ t - \frac{1}{2}gt^2 \\ = \frac{v_0 sin θx}{v_0 cos θ} - \frac{1}{2}\frac{gx^2}{v^2_0 cos^2 θ} \\ y = (tan θ)x - (\frac{1}{2} \times \frac{g}{v^2_0 cos^2 θ})x^2$

This is the equation representing the trajectory of Mr Karim during his jump.