Solve the problem.
-If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }$. During what interval of time will the rocket be higher than $147 \mathrm {~m}$ ?
A) $0

Question

Solve the problem.
-If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }$. During what interval of time will the rocket be higher than $147 \mathrm {~m}$ ?
A) $0 < t < 3$
B) $3 < t < 5$
C) $5 < t < 6$
D) $6 < t < 8$

Quizplus · Accepted Answer

To find when the rocket is higher than 147 m, set the height equation greater than 147 and solve for $t$: $-9.8t^2 + 78.4t > 147$. Rearranging gives $9.8t^2 - 78.4t + 147 < 0$. Factoring or using the quadratic formula yields the roots, which represent the times when the rocket is exactly 147 m high. Solving this inequality shows the rocket is above 147 m between $t = 3$ and $t = 5$ seconds.

Solve the Problem ttt Seconds Is Given By h=−9.8t2+78.4th = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }h=−9.8t2+78.4t

Solve the Problem $t$ Seconds Is Given By $h = - 9.8 \mathrm { t } ^ { 2 } + 78.4 \mathrm { t }$