(Solved): Kinematic Eq Question. Is all one question* Write the solutions to all problems on a separate page. ...

Write the solutions to all problems on a separate page. Upload the answers as a single pdf. Show all work for credit (write Known values. What you are looking for, any relevant theory/equations, and the math work) final answers should have units when relevant. 1a. (a) An athlete jumps from a running start making an angle of \( \theta=33^{\circ} \) with the ground and touches down a distance \( x=7 \) meters from takeoff. Find the athlete's initial jump speed and velocity \( \vec{v}_{0} \) in vector form assuming the athlete's center of mass is the same height above ground at takeoff and touchdown. (12 pts) (b) What if: The athlete instead lands with his center of mass \( 40 \mathrm{~cm} \) below what it was at takeoff. How much further would the jump go compared to part (a)? (16 pts) (c) How much height does the athletes gain at the peak of the jump? ( 8 pts) 1b. Two Particles \( A \) and \( B \) have a position relative to some arbitrary point \( E \). The position vector with respect to time are \( \vec{r}_{A E}=D(6) \hat{i}+F\left(4 t^{2}\right) \hat{j}, \vec{r}_{B E}=G(3 t) \hat{i}-H\left(t^{4}\right) \hat{j} \). Find the displacement, velocity, and acceleration of particle \( A \) relative to \( B \). What should the units be for the constants \( D, F, G \), and \( H \) ? (14 pts)