# math

Vernon Wells hits a baseball that travels for 142m before it lands. The flight of the ball can be modeled by a quadratic function in which x is the horizontal distance the ball has traveled away from Vernon, and h(x) is the height of the ball at that distance.

Assume that the ball was between 0.6m and 1.5m above the ground when it was hit:
a)What would be a good range of values for the height of the ball? are some values for the height unreasonable?
b)What happens when x=0?
c) What are the possible values for h(x) when x=0?
d)What would be a good range of values for the height of the ball? Are some values for the height unreasonable?

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1. (b) h(0) is the height at time 0: when the ball was hit

(c) so, 0.6 <= h(0) <= 1.5

(a) Since most balls are hit at a fairly low trajectory, I'd say that since the max height of the ball occurs at roughly 71 meters, that might be a good estimate for the height of the ball at that point.

(d) is exactly the same as (a). The maximum height is

(v sinθ)^2/(2g)

maybe you should investigate the speed at which baseballs are usually hit. Then since θ=45° gives the maximum possible height, use your value for v to get a greatest possible height of v^2/(4g).

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