SOLUTION: During training, a hurdler wants to raise the height of the hurdlers from the high school standard of 39 inches to the NCAA standard of 42 inches. His best race from last lesson in

Question 1181948: During training, a hurdler wants to raise the height of the hurdlers from the high school standard of 39 inches to the NCAA standard of 42 inches. His best race from last lesson included a clear over 39-inch hurdle that was modeled by h(t)=(-0.025t)(t-25), where t is time (in tenths of a sec) after his lead led left the track and h is the height (in feet)
a. If he runs as well as his best race last year, will this hurdler clear the new height? Why or why not
b. Why must the quadratic term in this model have negative coefficient?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the quadratic is h(t)=-0.025t^2+0.625t
this is a negative quadratic meaning it is convex upward and the vertex will be above the ground, which it must be. The runner is having to overcome the (negative) acceleration of gravity
The value of t at the vertex is at -b/2a =-0.625/-0.05=12.5
This is 12.5 tenths of a second
h(12.5)=-0.025*156.25+0.625(12.5)=3.90625 feet
The new height of 42 inches is 3.5 feet, so he will clear it by 0.4 feet or about 5 inches at the vertex.

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