Here we know that Margie is standing on a bridge looking at the river. She throws a rock over the bridge with an initial velocity of 60 ft/sec. The height, h, of the rock at the rime t seconds after it was thrown can be modeled by the equation:
[tex]h(t) = -16t^2+60t+72[/tex]
To calculate how long will it take for the rock to reach the surface of the water, we need to set [tex]h(t)=0[/tex]. So:
[tex]0 = -16t^2+60t+72 \\ \\ \\ \text{Using quadratic formula}: \\ \\ t=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ a=-16 \\ \\ b=60 \\ \\ c=72 \\ \\ \\ t=\frac{-60 \pm \sqrt{60^2-4(-16)(72)}}{2(-16)} \\ \\ t=\frac{-60 \pm \sqrt{60^2-4(-16)(72)}}{2(-16)} \\ \\ t=\frac{-60 \pm \sqrt{8208}}{-32} \\ \\ t_{1}=4.70 \\ \\ t_{2}=-0.95[/tex]
Given that time can't be negative, we just choose the positive value. Therefore, it will take 4.70 seconds for the rock to reach the surface water.
