$($A$4)[2$ pts each$]$ A projectile is fired from an initial height of $10$ m above the ground with and an initial velocity of $180\frac{m}{s}$ at an angle of elevation of $60.$

Use the equation $r(t)=($:$(v_{0}cos)t,h_0+(v_{0}sin)t-\frac{1}{2}g{t}^2$:$)$ and $g$~~$9\mathrm{.}81\frac{m}{s^2}$ to answer the following questions. Include units in your final answers.

a$.$ For what value of $t$ is the vertical component of $v(t)$ equal to $0?$ Round your answer to $4$ decimal places.

b$.$ Use your answer in part a to compute the maximum height the projectile reaches? Round your answer to $1$ decimal place.

c$.$ How long does it take the projectile to hit the ground? Round your answer to $4$ decimal places.

d$.$ Use your answer in part $c$ to compute the horizontal distance traveled by the projectile when it hits the ground. Round your answer to $1$ decimal place.