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# grasshopper jump

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The function y=-16t^2+8t represents the height y (in feet) of a grasshopper jumping straight up from the ground t seconds after the start of the jump. After how many seconds is the grasshopper 1 foot off the ground?

Jan 8, 2019
edited by Guest  Jan 8, 2019

#1
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When y = 0 the paintbrush hits the ground.

0=25-16t^2       solve for t

25=16t^2

25/16 = t^2

t = 5/4 sec      (the other solution for t^2)   -5/4 sec is invalid for a time

Jan 8, 2019
#2
+1

The function y=-16t^2+8t represents the height y (in feet) of a grasshopper jumping straight up from the ground t seconds after the start of the jump. After how many seconds is the grasshopper 1 foot off the ground?

We need to solve this

-16t^2+ 8t  =  1      subtract 1 from both sides

-16t^2 + 8t - 1  = 0           multiply through by - 1

16t^2 - 8t + 1 =  0           factor

(4t - 1) (4t - 1) = 0

(4t - 1)^2 =  0           take the square root

4t - 1 = 0       add 1 to both sides

4t  = 1           divide both sides by 4

t =  1/4   seconds   Jan 9, 2019