SOLUTION: A doctor squirts a small amount of liquid from a syringe vertically. If the liquid emerges with a velocity of 5.5 m/s how long does it take for the liquid to return to the level of

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Question 518949: A doctor squirts a small amount of liquid from a syringe vertically. If the liquid emerges with a velocity of 5.5 m/s how long does it take for the liquid to return to the level of the syringe and what is the maximum height it can reach?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Use the function:
h%28t%29+=+-4.9t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D
This is the function for determining the height (in meters) of an object (liquid in this case) propelled upwards with an initial velocity v%5B0%5D(in meters per second) from an initial height of h%5B0%5D (in meters) at time t (in seconds).
h%28t%29+=+-4.9t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D Substitute v%5B0%5D+=+5.5, h%5B0%5D+=+0 and h%28t%29+=+0 to find the time, t, at which the liquid will return to its initial height.
0+=+-4.9t%5E2%2B5.5t Factor a t.
t%28-4.9t%2B5.5%29+=+0 Apply the zero product rule.
t+=+0 This is the initial state.
-4.9t%2B5.5+=+0 Solve for t.
4.9t+=+5.5
t+=+1.12 seconds to return to its initial height at the doctor's syringe.
To find the maximum height of the object (liquid), you need to find the vertex of the parabola which is the graph of the equation:
h%28t%29+=+-4.9t%5E2%2B5.5t This graphs into a parabola that opens downward so its vertex will be the maximum height.
h%28t%29+=+-4.9t%5E2%2B5.5t The value of t at the vertex is given by:
t+=+-b%2F2a where b = 5.5 and a = -4.9
t+=+%28-5.5%29%2F2%28-4.9%29
t+=+0.56 seconds. This is the time at which the object reaches its maximum height. Substitute this into the function for the height to find the maximum height in meters.
h%280.56%29+=+-4.9%280.56%29%5E2%2B5.5%280.56%29
h%280.56%29+=+1.54 meters.