A penny is thrown from the top of a 26.6-meter building and hits the ground 3.59 seconds after it was thrown. The penny reached its maximum height above the ground 0.77 seconds after it was thrown.

1. Define a quadratic function, h, that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t.

2.What is the maximum height of the penny above the ground?

The quadratic function which models the motion of the penny is h(t) = -4.9t² + 10.18t + 26.6 and the maximum height reached is 31.53 meters

The relationship can be expressed in the form :

h(t) = - 0.5gt² + vt + h (downward motion)

g = 9.8 m/s²

h = 26.6 m

v = ?

We can obtain v thus ;

h(t) = -0.5gt² + vt + 26.6

h(t) = - 4.9t² + vt + 26.6

Time when penny hits the ground ; t = 3.59

h(3.59) = 0

0 = -4.9(3.59)² + v(3.59) + 26.6

− 63.15169 + 3.59v + 26.6 = 0

3.59v = 36.55169

v = 36.55169 /3.59

v = 10.181 m/s

Equation becomes :

h(t) = -4.9t² + 10.18t + 26.6

2.) The maximum height of the penny above the ground ;

t = 0.77 seconds

h(0.77) = -4.9(0.77^2)+ 10.18(0.77) + 26.6

Maximum height reached = 31.53 meters

Therefore, the maximum height reached is 31.53 meters

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