A ball has been dropped from the top of a building Its heigh

A ball has been dropped from the top of a building. Its height (in feet) after t seconds is given by the function H (t) = -16t^2 + 256. What is the height of the ball after 2 seconds? H (2) = How far will the ball travel during the third second? H (2) - H (3) = How tall is the building? H (0) = When will the ball hit the ground? |0 = -16t^2 + 256 rightarrow t =

Solution

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H(t) = - 16t² + 256

a] at t = 2, the height of the ball can be found if we substitute t = 2 in the expression for H(t)

H(2) = - 16(2)² + 256 = 192 ft

b] H(2) = 192 ft

H(3) = - 16(3)² + 256 = 112 ft

therefore, H(2) - H(3) = 192 - 112 = 80 ft.

thus the ball travelled a distance of 80ft in the 3^rd second.

c] H(0) = - 16(0)² + 256 = 256 ft

so the building is 256 ft tall.

d] 0 = - 16t² + 256

16t² = 256

=> t² = 16

t = 4 s

so the time taken by the ball to hit the ground will be 4 seconds.