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Question

# Cargo is tied with rope on the roof of a 4.5-foot-tall car. The car is traveling down a road at 42 mph and hits a concrete barrier. The rope snaps, allowing the cargo to propel forward. Use the equations $y=-16.1 t^{2}+4.75$ and $y=-0.0042 x^{2}+4.75$ where y represents height in feet, x represents horizontal distance in feet, and t represents time in seconds, to find the time it takes for the cargo to hit the ground and the horizontal distance it travels.

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Cargo is tied with rope on the roof of a $4.5$-foot-tall car. The car is traveling down a road at $42$ mph and hits a concrete barrier. The rope snaps, allowing the car got opropel forward. Use the equations,

\begin{align*} y=-16.1t^2+4.75\\ y=-0.042x^2+4.75\\ \end{align*}

where y represents height in feet,x represents horizontal distance in feet, and t represents time in seconds, to find the time it takes for the cargo to hit the ground and the horizontal distance it travels.To calculate $t$ we will use that is $y=0$ because the cargo will height $0$ after impact to the ground. So. we have,

\begin{align*} 0=-16.1t^2+4.75\\ -4.75=-16.1t^2\\ t^2=\dfrac{-4.75}{-16.1}=0.30\\ t=\sqrt{0.30}=0.55\,\,\text{seconds} \end{align*}

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