A Helicopter Rises Straight Up in the Air So That $\mathrm { v } ( \mathrm { t } ) = \mathrm { t } ^ { 3 / 2 } + \frac { 1 } { 2 } \mathrm { t } ^ { 1 / 2 } + 1$

A helicopter rises straight up in the air so that its velocity t seconds after take-off is $\mathrm { v } ( \mathrm { t } ) = \mathrm { t } ^ { 3 / 2 } + \frac { 1 } { 2 } \mathrm { t } ^ { 1 / 2 } + 1$ feet per second. If the landing pad is 100 feet above the ground, which of the following gives the height of the helicopter at time t ?

A) h(t) = $\frac { 5 } { 3 }$ $t ^ { 5 / 2 }$ + $\frac { 3 } { 4 }$ $t ^ { 3 / 2 }$ + t - 100
B) h(t) = $\frac { 2 } { 5 }$ $t ^ { 5 / 2 }$ + $\frac { 1 } { 3 }$ $t ^ { 3 / 2 }$ + t + 100
C) h(t) = $\frac { 3 } { 2 }$ $t 1 / 2$ + $\frac { 1 } { 4 }$ $t ^ { - 1 / 2 }$ + 100
D) h(t) = $\frac { 2 } { 3 }$ $t ^ { 5 / 2 }$ + $\frac { 1 } { 4 }$ $t ^ { 3 / 2 }$ + t + C
E) none of these