SOLUTION: I am getting frustrated trying to figure this out. Can someone please break down the steps? Solve.​ (Use 4.9tsquared+v0t=​s.) a) A bolt falls off an airplane at an

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Question 1127955: I am getting frustrated trying to figure this out. Can someone please break down the steps?
Solve.​ (Use 4.9tsquared+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 40 ​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 6 ​sec, when thrown downward at an initial velocity of 40 ​m/sec from a​ plane?
​a) It takes the bolt ________sec m/sec to reach the ground.
b)
c)
Found 2 solutions by MathLover1, ankor@dixie-net.com:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
s=4.9t%5E2%2Bv%5B0%5Dt
a) A bolt falls off an airplane at an altitude of 500m. Approximately how long does it take the bolt to reach the​ ground?
s=4.9t%5E2+%2B+v%5B0%5Dt where
s = the distance above ground (the height or altitude),
t+= time in seconds, and
v%5B0%5D is the initial velocity (zero in this case).
4.9t%5E2+=+500 Divide both sides by 4.9
t%5E2+=+500%2F4.9
t%5E2+=+102.04082
t+=+sqrt%28102.04082%29
t+=+10.10s

b) A ball is thrown downward at a speed of 40%28m%2Fs%29 from an altitude of 500m. Approximately how long does it take the ball to reach the ground?
Always assume positive = up and negative = down.
So the acceleration of gravity is *always* negative:
a=-9.81%28m%2Fs%5E2%29 (acceleration due to gravity)
In your problem, the object lands 500m below the starting point, so
s=-500
v%5Bi%5D%29=40%28m%2Fs%29
Use this equation:
s=v%5Bi%5D%29t%2B%281%2F2%29a%2At%5E2
-500=40%28m%2Fs%29t%2B%281%2F2%29%28-9.81%28m%2Fs%5E2%29%29%2At%5E2....we have to find the time t
-500=40%28m%2Fs%29t-4.905%28m%2Fs%5E2%29%2At%5E2
4.905%28m%2Fs%5E2%29%2At%5E2-40+%28m%2Fs%29t-500=0
t ≈ 14.9661s

c) Approximately how far will an object fall in 6sec, when thrown downward at an initial velocity of 40%28m%2Fs%29 from a plane?
v%5Bi%5D%29=40+%26%238203%3B%28m%2Fsec%29
t=6s
s=+40%2A6%2B%281%2F2%299.81%2A6%5E2..............a=g=9.81%28m%2Fs%5E2%29
s=240+%2B176.58
s=416.58m

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
olve.​ (Use 4.9tsquared+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?
:
there is no upward velocity, the ground = 0, therefore
-4.9t^2 + 500 = 0
-4.9t^2 = -500
t^2 = -500/-4.9
t^2 = 102.04
t = sqrt%28%28102.04%29%29
t = 10.1 sec for the bolt to hit the ground when dropped by the plane
:
:
​b) A ball is thrown downward at a speed of 40 ​m/sec from an altitude of 500 m. Approximately how long does it take the ball to reach the​ ground?
:
thrown downward it's -40 m/sec
-4.9t^2 - 40t + 500 = 0
use the quadratic formula; a=-4.9; b=-40; c=500
the positive solution
t = 6.8 sec for the ball to reach the ground when thrown downward
:
;
c) Approximately how far will an object fall in 6 ​sec, when thrown downward at an initial velocity of 40 ​m/sec from a​ plane?
4.9(36) + 40(6) = 416.4 meters in 6 sec
:
;