$(8\%)$ Problem $8$: A student launches a small rocket which starts from rest at ground level. At a height $h=1\mathrm{.}29km,$ the rocket

reaches a speed of $v_f=226\frac{m}{s}.$ At that height, the rocket runs out of fuel, so there is no longer any thrust propelling it$.$ Take the

positive direction to be upward. The drawing is not to scale.

$33\%$ Part $($a$)$ Assuming constant acceleration, what is the rocket's acceleration, in meters per squared second, during the period from its launch until it runs out

of fuel?

$a_1=19\mathrm{.}80\frac{m}{s^2}$

$$ Correct!

$33\%$ Part $($b$)$ After the rocket's engine turns off at a height of

$h=1\mathrm{.}29km,$ it continues to move upward due to the velocity that it reached. What is the rocket's acceleration, in meters per squared second, during the period from

engine shutoff until it returns to the ground? Ignore air resistance.

$a_2=-9\mathrm{.}8$

$a_2=-9\mathrm{.}800\frac{m}{s^2}$

$33\%$ Part $($c$)$ Calculate the maximum height, in meters above ground level, that the rocket reaches.