For example, on May $7,1992,$ the space shuttle Endeavor was launched on mission STS$-49,$ the purpose of which was to install a new perigee kick motor in an Intelsat communications satellite. The table, provided by NASA, gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use this data to estimate an upper bound for the space shuttle Endeavor's height above Earth's surface $60$ seconds after liftoff. $\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|\}$

$\backslash$hline Event & Time $($s$)$ & Velocity $($ft$/$s$)\backslash \backslash$

$\backslash$hline Launch & $0$ & $0\backslash \backslash$

$\backslash$hline Begin roll maneuver & $8$ & $178\backslash \backslash$

$\backslash$hline End roll maneuver & $15$ & $338\backslash \backslash$

$\backslash$hline Throttle to $89\backslash \%$ & $18$ & $430\backslash \backslash$

$\backslash$hline Throttle to $67\backslash \%$ & $30$ & $754\backslash \backslash$

$\backslash$hline Throttle to $104\backslash \%$ & $55$ & $1,362\backslash \backslash$

$\backslash$hline Maximum dynamic pressure & $60$ & $1,461\backslash \backslash$

$\backslash$hline Solid rocket booster separation & $129$ & $4,231\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$