## anonymous one year ago tennisball mashine shoots a ball straight up in the air, it lands after 7 seconds What's the hight of the ball given v=f(t)=30-10t i figured that the equation i got is actually the derivative of -5t^2+30t ball shots upp with a velocity of 30m/s, is a physics mix i have no pheta angle neede to solve it in a simpler way...vertex apex im asked: what does 30 stand for? -10t?acceleration? and what's max height? i have a graf with and dowsslopping linear line crossing the y axis at 30m/s and the x axis at 3 seconds

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1. anonymous

ok tell me V=30-10t did they give you this with question

2. anonymous

oh ok now i can solve it

3. anonymous

4. anonymous

because you just sub 7 into original equation and you will get maximum height

5. anonymous

$=-5(7)^{2}+30 \times 7$

6. IrishBoy123

yes, for $$v(t) =30 - 10t$$ we have 30 as initial velocity, -10 for gravity (acceleration) so as you say $$x(t) =30t - 5t^2+x_0 = 5t(6-t)+x_0$$ but note the integration constant if it lands after t = 7, then $$\large x(7) = x_0-35$$ !!!!! weird! is the machine 35m above gound or does the ball land in a crater?!?! anyways, at the peak of its flight $$v(t) = 0 \implies 30 - 10t=0, t = 3$$ solve from there