+203 A ball is thrown upward from the roof of a building 60m tall. The ball reaches a height of 80m above the ground after 2s and hits the ground 6s after being thrown.
a)sketch a graph that shows the height of the ball as a function of time (done) (0,60)to(6,0)
b)state the domain and range D={xer|0<=x<=6} R={yer|0<=y<=80}
This one I dont get
c) Determine an equation for the function.
I used f(x)=a(x-2)2+80 but when I input a point the answer is never correct.
+6252 You need to know the basic equation of ballistic motion
h(t)=−gt22+v0t+h0
here they give you h0=60
they also seem to be using g=−10 m/s2 which isn't quite accurate but close enough for government work.
You have two equations
h(2)=80, h(6)=0you really only need one of them, plugging in values we have80=−5(22)+2v0+6020=2v0−20v0=20checking with the other equation we haveh(6)=−5(62)+20(6)+60=−180+120+60=0 as expected. So our equation of motion ish(t)=−5t2+20t+60we can rewrite this ash(t)=−5(t2−4t−12)=−5((t−2)2−4−12)=−5(t−2)2+80and this last is the standard form of the parabola
