A ball is tossed into the air from an initial height of three meters and reach i

Question

A ball is tossed into the air from an initial height of three meters and reach its maximum height of 15 meters in two seconds.
A) determine the quadratic model that gives the height as a function of the time in seconds
B) how long will it spend in the air A ball is tossed into the air from an initial height of three meters and reach its maximum height of 15 meters in two seconds.
A) determine the quadratic model that gives the height as a function of the time in seconds
B) how long will it spend in the air
A) determine the quadratic model that gives the height as a function of the time in seconds
B) how long will it spend in the air

Explanation / Answer

h = a + bt + ct^2

h(0) = 3 , h(2) = 15 and v(2) = h'(2) = 0  

a = 3

15 = 3 + 2b+ 4c

b+ 2c = 6

v(t) = h'(t) = b+2ct

b+ 4c = 0

solving we get

c = -3

b = 12

hence

h = 3 + 12 t -3t^2

b) h = 0

or 3 + 12 t -3t^2 = 0

t = 2 + sqrt(5) sec

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