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) write the equation for the function

b) state the domain and range of the function

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Using `uarrv = u+at` for upward travel until it reach 80m above ground. Consider g = 10m/s

`0 = u-10xx2`

`u = 20m/s`

Consider rooftop as datum.

`S = ut+1/at^2`

`S = 20t-5t^2`

Then you know maximum the ball can reach is 20m top from roof and minimum is 60 below roof.

So the range will be `-60<=S<=20`

You know that the ball will travel for 6s. So the domain would be;

`0<=t<=6`

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