SOLUTION: an object is projected straight up with an initial velocity of k ft. /sec. The height of the object, h, at any time, t, is given by the function h(t)= -16t^2+ kt. if the object ret

Question 1111603: an object is projected straight up with an initial velocity of k ft. /sec. The height of the object, h, at any time, t, is given by the function h(t)= -16t^2+ kt. if the object returns to the ground at t=8 sec., find the height (in feet) of the object at t=7 sec.Explain in words your steps to finding the value of k.
I tried to find k but i could finish because i didn't know what to do after u plug in the numbers and simplify also i got a crazy number when i didn't simplify
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
an object is projected straight up with an initial velocity of k ft. /sec. The height of the object, h, at any time, t, is given by the function h(t)= -16t^2+ kt. if the object returns to the ground at t=8 sec., find the height (in feet) of the object at t=7 sec.Explain in words your steps to finding the value of k.
I tried to find k but i could finish because i didn't know what to do after u plug in the numbers and simplify also i got a crazy number when i didn't simplify
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IDK what you mean by a "crazy number."
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h(t)= -16t^2+ kt
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A total flight time of 8 sec --> 4 seconds ascending and 4 second descending.
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--> max height at 4 seconds
Falling for 4 seconds --> h(4) = 16*4^2 = 256 feet for max height.
Max height is the vertex of the parabola.
Vertex is at t = -b/2a = -k/-32 @ t=4
4 = k/32
k = 128 ft/sec --- the launch speed
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find the height (in feet) of the object at t=7 sec.
h(t) = -16t^2 + 128t
h(7) = -16*49 + 128*7 = 896 - 784 = 112 feet
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PS h(7) = h(1) = -16 + 128 = 112 feet

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
an object is projected straight up with an initial velocity of k ft. /sec.
The height of the object, h, at any time, t, is given by the function h(t)= -16t^2+ kt.
if the object returns to the ground at t=8 sec., find the height (in feet) of the object at t=7 sec.
Explain in words your steps to finding the value of k.
:
When it hits the ground h(t) = 0, when t = 8
-16(8^2) + 8k = 0
-16(64) + 8k = 0
-1024 + 8k
8k = 1024
k = 1024/8
k = 128
"find the height when t = 7 sec
h(t) = -16(7^2) + 128(7)
h(t) = -784 + 896
h(t) = 112 ft, height at 7 sec
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