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malfutka [58]
3 years ago
10

Margie is standing on a bridge looking at the river below. She throws a rock over the bridge with an initial

Mathematics
1 answer:
Marina CMI [18]3 years ago
6 0
<h2>Explanation:</h2><h2></h2>

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:

h(t) = -16t^2+60t+72

To calculate how long will it take for the rock to reach the surface of the water, we need to set h(t)=0. So:

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

Given that time can't be negative, we just choose the positive value. Therefore, <em>it will take 4.70 seconds for the rock to reach the surface water.</em>

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