A penny is thrown from the top of a 60.8-meter building and hits the ground 2.78

Question

A penny is thrown from the top of a 60.8-meter building and hits the ground 2.78 seconds after it was thrown. The penny reached its maximum height above the ground 0.58 seconds after it was thrown. a. 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 Yas thrown, t. Preview b. What is the maximum height of the penny above the ground? Preview Points possible: 10 Unlimited attempts. License ost this question to forum

Explanation / Answer

penny is thrown from top of 60.8 metre

hits ground after 2.78 seconds

maximum height is reached at 0.58 seconds

x cooridinate of vertex = 0.58

zero = (2.78 , 0 )

y intercept = ( 0 , 60.8 )

so , y = a ( x - 0.58)^2 + k

plugging the value of (2.78,0)

0 = a ( 2.78 - 0.58)^2 + k

0 = 4.84a + k

plugging the value of ( 0, 60.8 )

60.8 = a ( 0.58)^2 + k

60.8 = .3364 a + k

solving the two equations

4.5036a = - 60.8

a = -13.5

k = 65.3414

equation is

h = -13.5 ( t - 0.58)^2 + 65.3414

b) maximum height = 65.3414 metres

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