A toy rocket is launched vertically from ground level $($y $=0$ m$.,$ at time t $=0\mathrm{.}0$ s$).$ The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to $64$ m and acquired a velocity of $60$ m$/$s$.$ The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground. The time interval, during which the rocket engine provides upward acceleration, is closest to:

a$.$

$1\mathrm{.}5$ s

b$.$

$1\mathrm{.}7$ s

c$.$

$2\mathrm{.}1$ s

d$.$

$2\mathrm{.}3$ s

e$.$

$1\mathrm{.}9$ s