Re: Projectile Question

In article <Ken.Pledger-759035.09533411082005@xxxxxxxxxxxxxxxxxx>,
Ken Pledger <Ken.Pledger@xxxxxxxxxxxxx> wrote:
[...]
>> Question is. A ball is kicked horizontal distance of 50m. Max height
>> of 25m with flight time of 4 seconds. Calculate angle ball was kicked
>> at.
[...]
> Thank you for posting your reasoning. I agree that there are too
>many constraints chasing too few unknown parameters to fit them.
>However, I did manage to find a solution by treating g as another
>unknown. [...]

I agree that the question as posed is not well worded ...!
But you both seem to be assuming that the position of the ball after
4s is 50m away horizontally *and* 0m away vertically. If so, then
the trajectory of the ball is determined simply by the distances, the
timing is irrelevant [except to determine g!] and the angle of launch
is atan(2) ["y = x*(50-x)/25", so "dy/dx = 2-2x/25"].

But if we remove the "*and*" clause, then the initial vertical
speed is "sqrt(2gh) ~ sqrt (2*9.8*25) = 7 sqrt(10)" m/s, the horizontal
speed is 50/4 m/s, so the angle of launch is atan(0.56 sqrt(10)) [E&OE].
After 4s, the ball is at (50, 20 sqrt(2g) - 8g) ~ (50,10).

Of course, all bets are off if air resistance is to be taken
into account.

--
Andy Walker, School of MathSci., Univ. of Nott'm, UK.
anw@xxxxxxxxxxxxxxxx
.

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