Problem $6.$

An athlete performs a standing broad jump. $($In a standing broad jump, you start from a stationary position and push off with your legs to jump a horizontal distance.$)$ To start the jump, the athlete crouches down so that he can use his legs to generate a force $($P$)$ that pushes him off the ground and forward $($see Figure a$).$ The force $P$ that the athlete generates is equal to twice his weight and acts at an angle $=65$ to the ground. The weight of the athlete is $600N$ and is represented by the vector $W$ in Figure b$.$

a$.$ What is the magnitude of the net force $(F_{\text{n}\text{e}\text{t}})$ acting on the athlete? What is the angle $$ of $F_{\text{n}\text{e}\text{t}}?$ What acceleration will $F_{\text{n}\text{e}\text{t}}$ produce?

Problem $6.$ continued

$0.$ The athlete's center of gravity $($C$.$G$)$ is displaced a distance of $0\mathrm{.}6m($see Figure c$)$ as he straightens his legs to jump. $(F_{\text{n}\text{e}\text{t}}$ accelerates the C$.$G$.$ over this distance.$)$ What will the takeoff velocity be$?$ The takeoff velocity is the athlete's velocity the instance his feet leave the ground.

c$.$ What horizontal distance will the athlete jump? The path of the jump can be approximated as a projectile motion, with air resistance negligible.

Note: Athletes will use their arms to help them jump further, but that's beyond the scope of this analysis.