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) (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
===========================
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
====================
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) (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
--------------------
Answer: 10.1015 seconds (this is approximate)
=======================================================
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
or
or
or
or
or
or
Toss out the negative t value (negative time values make no sense)
--------------------
Answer: 9.1325 seconds (approximate)
=======================================================
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
--------------------
Answer: 4313.6 feet
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