SOLUTION: Please help; I am having great difficulty with this one. Solve.​ (Use 4.9t^2+v0t=​s.) ​a) A bolt falls off an airplane at an altitude of 500 m. Approximatel

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Question 1128492: Please help; I am having great difficulty with this one.
Solve.​ (Use 4.9t^2+v0t=​s.)
​a) A bolt falls off an airplane at an altitude of 500 m. Approximately how long does it take the bolt to reach the​ ground?
​b) A ball is thrown downward at a speed of 10 ​m/sec from an altitude of 500 m. Approximately how long does it take the ball to reach the​ ground?
​c) Approximately how far will an object fall in 8 ​sec, when thrown downward at an initial velocity of 10 ​m/sec from a​ plane?
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use 4.9t^2 + v0t = s
a) A bolt falls off an airplane at an altitude of 500 m. Approximately how long does it take the bolt to reach the ground?
s = 4.9t^2 + v0t = 500
4.9t^2 = 500
t = sqrt(500/4.9) =~ 10.1 seconds
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b) A ball is thrown downward at a speed of 10 m/sec from an altitude of 500 m. Approximately how long does it take the ball to reach the ground?
Use s = -4.9t^2 + v0t --- It's -4.9t^2 as gravity acts downward
---
At impact, s = 0
s = -4.9t^2 + 10t = 0
t = 0 --- ignore
t = 10/4.9 = 2.041 seconds at impact
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c) Approximately how far will an object fall in 8 sec, when thrown downward at an initial velocity of 10 m/sec from a plane?
s = -4.9t^2 - 10t --- both terms are downward --> both negative
Sub 8 for t, find s

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Part A)

v = initial velocity = 0
s = 500 = vertical distance the object travels (from plane to ground)

Plug in the given values and solve for t
4.9t^2 + v*t = s
4.9t^2 + 0*t = 500
4.9t^2 + 0 = 500
4.9t^2 = 500
t^2 = 500/4.9
t^2 = 102.04081632653
t = sqrt(102.04081632653)
t = 10.101525445522
t = 10.1015

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Answer: 10.1015 seconds (this is approximate)

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Part B)

v = 10
s = 500
like in part A, the goal is to solve for t

First plug in the values and get everything to one side
4.9t^2 + v*t = s
4.9t^2 + 10*t = 500
4.9t^2 + 10*t - 500 = 0

Then use the Quadratic Formula with a = 4.9, b = 10, c = -500
t+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 or t+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
t+=+%28-10%2Bsqrt%28%2810%29%5E2-4%284.9%29%28-500%29%29%29%2F%282%284.9%29%29 or t+=+%28-10-sqrt%28%2810%29%5E2-4%284.9%29%28-500%29%29%29%2F%282%284.9%29%29
t+=+%28-10%2Bsqrt%289900%29%29%2F%289.8%29 or t+=+%28-10-sqrt%289900%29%29%2F%289.8%29
t+=+%28-10%2B99.498743710662%29%2F%289.8%29 or t+=+%28-10-99.498743710662%29%2F%289.8%29
t+=+%2889.498743710662%29%2F%289.8%29 or t+=+%28-109.498743710662%29%2F%289.8%29
t+=+9.1325248684349 or t+=+-11.1733411949655

Toss out the negative t value (negative time values make no sense)

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Answer: 9.1325 seconds (approximate)

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Part C)

v = 10
t = 8
s = unknown

Plug in the given values and compute
4.9t^2 + v*t = s
s = 4.9t^2 + v*t
s = 4.9*8^2 + 500*8
s = 4.9*64 + 500*8
s = 313.6 + 4000
s = 4313.6

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Answer: 4313.6 feet