Solve the problem.
-If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }$. During what interval of time will the rocket be higher than $205.8 \mathrm {~m}$ ?
A) $7

Question

Solve the problem.
-If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }$. During what interval of time will the rocket be higher than $205.8 \mathrm {~m}$ ?
A) $7 < t < 6$
B) $0 < t < 3$
C) $3 < t < 7$
D) $6 < t < 10$

Quizplus · Accepted Answer

To find when the rocket is higher than 205.8 m, set the height equation greater than 205.8 and solve for $t$: $-9.8t^2 + 98t > 205.8$. Rearranging gives $9.8t^2 - 98t + 205.8 < 0$. Factoring or using the quadratic formula gives the roots as $t = 3$ and $t = 7$. Therefore, the rocket is higher than 205.8 m between 3 and 7 seconds.

Solve the Problem ttt Seconds Is Given By h=−9.8t2+98th = - 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }h=−9.8t2+98t

Solve the Problem $t$ Seconds Is Given By $h = - 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }$