If a rocket is propelled upward from ground level, its height in meters after t seconds is given by $h ( t ) = - 9.8 t ^ { 2 } + 49 t$
During what interval of time will the rocket be higher than 58.8m ?
A) 3

Question

If a rocket is propelled upward from ground level, its height in meters after  t  seconds is given by $h ( t ) = - 9.8 t ^ { 2 } + 49 t$
During what interval of time will the rocket be higher than  58.8m  ?
A)  3<t<4 
B)  4<t<5 
C)  0<t<2 
D)  2<t<3

Quizplus · Accepted Answer

To find when the rocket is higher than 58.8m, we set the height equation greater than 58.8 and solve for $t$: $-9.8t^2 + 49t > 58.8$. Rearranging gives $9.8t^2 - 49t + 58.8 < 0$. Factoring or using the quadratic formula, we find the roots of the equation $9.8t^2 - 49t + 58.8 = 0$ are approximately $t = 2$ and $t = 3$. Therefore, the rocket is higher than 58.8m between 2 and 3 seconds.

If a Rocket Is Propelled Upward from Ground Level, Its h(t)=−9.8t2+49th ( t ) = - 9.8 t ^ { 2 } + 49 th(t)=−9.8t2+49t

If a Rocket Is Propelled Upward from Ground Level, Its $h ( t ) = - 9.8 t ^ { 2 } + 49 t$