Expert: Sherman D. - 11/30/2008

Question
Please, help me with this. I do not understand if I have to include initial velocity or not. Is it the simple S=V.T or S=V0.T-16.Tsquare??
A young man throws fish upward to a seagull to catch ad a velocity of 50'"/sec. He is standing on a pier that is 25' above the ocean surface. The seagull is 100' above the ocean surface.
a. Write an equation to model this situation.
b. How many sec later does the seagull catch the fish after it is tossed upwards?
c. If the seagull is to miss the fish, what is the greatest height the fish fly to and how long does it take to get there.

Answer
S(T) = -16T^2 + VoT + So

100 = -16T^2 + 50T + 25

-16T^2 + 50T - 75 = 0

the reason i put 100 on the left is because that is suppose to be the height at which the bird is to catch the fish.

Using the quadratic formula

T = (-50 +/- sqrt(50^2 + 4(-16)(-75)))/(2(-16))
T = (-50 +/- sqrt(2500 + 4800))/-32
T = (-50 +/- sqrt(7300))/-32
T = (-50 +/- 10sqrt(73))/-32
T = about 4.233 seconds.

T = (-50)/(2(-16))
T = 50/32
T = 25/16

-16(25/16)^2 + 50(25/16) + 25 = 64 1/16ft

so to answer a-c

A.)
S = -16T^2 + 50T + 25

B.)
about 4 seconds

C.)
64ft and .75inches

info found at
www.algebralab.org/Word/Word.aspx?file=Algebra_MaxMinProjectiles.xml

if you would like to make sure this is correct, check with answers.yahoo.com, and for your title use Velocity, Time, Height and Quadratic Equations.