a ball thrown from the top row of seats. the function h(t)=16t^2+80t+96 give the hight in feet, of the ball t seconds after it is thrown. how long does it take before the ball hits the ground?
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When h(t)=0 the ball reaches the ground, so 16(t²+5t+6)=0, so t²+5t+6=0=(t+3)(t+2)  which gives us negative values for t, so I suspect that 16t² should be -16t².

So we would have -t²+5t+6=0, that is, t²-5t-6=0=(t-6)(t+1) and t=6 seconds is the time the ball takes to reach the ground. We ignore t=-1 as meaningless (time before the ball was thrown).

The constant 96 feet is the height of the top row of seats. -16t² is the negative effect of gravity on the ball and  80 feet per second is the vertical component of the speed the ball was thrown. This is how h(t) was constructed.

by Top Rated User (696k points)

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