Thread: parabola ball

a tennis player heyton lewitt, is able to out think his opponents by hitting a shot and making the opposition think that it will go out but instead it lands perfectly on the base line (15m from net). his opponent saw through this plan and was able to mentally calculate that the path followed the ball corresponded to the mathematical equation of...

y= -x2 + 29.9x + 3
(y= negative x squared plus 29.9x plus three)

Q1.
Iva is 14.9m from the net and hits the ball straight back so that the tennis ball just missed the net which is 1metre high. is this a safe shot.. will it land it?

Q2.
construct a better shot for Heyton that would still give him a similar advantage but not be as obvious that he may have been a drug cheat.

PLEASE HELP ME!

Q0) What an odd question and WOW!!! That IS quite a shot. Can you determine the maximum height fo the ball? That WILL reach the cheap seats!

Q1) This is a bit tricky. It just isn't clear who is on which end of the equation. I think the orientation is most logicak if Mr. Lewitt is on his baseline at 0 and Iva's baseline is at 30. This makes the ball land EXACTLY onthe baseline. Hitting the ball at only 29.9, then, requires Iva to stretch to a height of -(29.9)^2 + 29.9(29.9) + 3 = 3 metres. Can this be done? Maybe. In any case, a drop of 2 meters in 14.9 certainly would have the ball land in bounds. Wheter or not this is "safe" remains a question. Does Iva mind if the ball comes back in hsi face?

Q2) Construct ANY parabola where the x-intercepts are the same but the maximum height is significantly LESS thatn 100 meters.

for Q1. a formula is needed to prove wether the shot would safely land in or not. not sure what formula i could use...?

also for Q2. not sure what you mean by constructing the parabola. could you show me how to do that please.