Suppose the stone is thrown at an angle of $27\mathrm{.}0$ below the horizontal from the same building $(h=50\mathrm{.}0m)$ as in the example above. If it strikes the ground $75\mathrm{.}3m$ away, find the following. $($Hint: For part $($a$),$ use the equation for the $x-$displacement to eliminate ${}_{0}t$ from the equation for the $y-$displacement.$)$

$($a$)$ the time of flight

The $x$ coordinate as a function of time is $x(t)=cos(27\mathrm{.}0)t,$ so the initial speed is $27.0t),$ where $x=75\mathrm{.}3$ and $t$ is the time of flight. Insert this into your equation for $y(t)$ and solve for the time of flight. Note that the answer should be smaller than $3\mathrm{.}1943828249997,$ since the stone is thrown down $($and to the right$).s$

$($b$)$ the initial speed $[$

Make sure you have a fixed coordinate system. For instance, is the origin $(0,0)$ at the base of the building? If so$,$ then the initial height of the stone is $50\mathrm{.}0m.$ Is the origin instead at the initial position of the stone? If so$,$ then the stone lands when its $y$ coordinate is equal to $-50\mathrm{.}0m.\frac{m}{s}$

$($c$)$ the speed and angle of the velocity vector with respect to the horizontal at impact

What is the initial velocity? Is either component negative? Which component changes with speed time? How does it change? What equations govern the changes in the components of velocity? If you know the components of the final velocity, can you find its magnitude and direction? $\frac{m}{s}$

What is the initial velocity? Is either component negative? Which component changes with angle time? How does it change? What equations govern the changes in the components of velocity? If you know the components of the final velocity, can you find its magnitude and direction?o below the horizontal

$3.$ Points Suppose the stone is thrown at an angle of $27\mathrm{.}0\backslash$deg below the horizontal from the same building $($h $=50\mathrm{.}0$ m$)$ as in the example above. If it strikes the ground $75\mathrm{.}3$ m away, find the following. $($Hint: For part $($a$),$ use the equation for the x$-$displacement to eliminate v$0$t from the equation for the y$-$displacement.$)($a$)$ the time of flight. $($b$)$ the initial speed. $($c$)$ the speed and angle of the velocity vector with respect to the horizontal at impac