Solve the problem.
-If a rocket is propelled upward from ground level, its height in meters after t seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 58.8 \mathrm { t }$. During what interval of time will the rocket be higher than $78.4 \mathrm {~m}$ ?
A) $4

Question

Solve the problem.
-If a rocket is propelled upward from ground level, its height in meters after t seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 58.8 \mathrm { t }$. During what interval of time will the rocket be higher than $78.4 \mathrm {~m}$ ?
A) $4 < t < 6$
B) $2 < t < 4$
C) $4 < \mathrm { t } < 4$
D) $0 < t < 2$

Quizplus · Accepted Answer

To find when the rocket is higher than 78.4 m, we set the height equation greater than 78.4 and solve for t: $ - 9.8t^2 + 58.8t > 78.4 $. Rearranging gives $ - 9.8t^2 + 58.8t - 78.4 > 0 $. Factoring or using the quadratic formula, we find the roots of the equation $ - 9.8t^2 + 58.8t - 78.4 = 0 $ to determine the interval where the height is greater than 78.4 m. Solving, we find that the rocket is above 78.4 m between 2 and 4 seconds.

Solve the Problem h=−9.8t2+58.8th = - 9.8 \mathrm { t } ^ { 2 } + 58.8 \mathrm { t }h=−9.8t2+58.8t

Solve the Problem $h = - 9.8 \mathrm { t } ^ { 2 } + 58.8 \mathrm { t }$