SOLUTION: 6. Speeding Bullet Problem: The speed of a bullet is traveling depends on the number of feet the bullet has traveled since it left the gun. The bullet is traveling at 3500 ft./sec.

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Question 653189: 6. Speeding Bullet Problem: The speed of a bullet is traveling depends on the number of feet the bullet has traveled since it left the gun. The bullet is traveling at 3500 ft./sec. when it is 25 feet from the gun, and at 2600ft./sec., it is 250 feet away.
a.) Write the particular equation expressing the speed of the bullet (s) in terms of its distance from the gun (d)
b.) How fast is the bullet going when it has traveled 300 ft?
c.) How far has the bullet traveled when it has slowed to 500 ft. / second
d.) What is the speed of the bullet immediately after the trigger is pulled?
e.) When the bullet has stopped, how far has it traveled?
f.) What is the slope? what does this number represent?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You are told the speed of the bullet is dependent on the distance from the gun. When the gun is fired, the bullet has some speed at a distance of 0. Let us call that initial speed S(0) (Speed at Distance of 0). We want to create an equation that gives the speed at any given distance after the gun is fired.
S%28t%29+=+S%280%29+%2B+mD%28t%29
Now we need to use the given information to find m and S(0). m is the slope. Since we are told the equation is linear and we are given two data points, we can calculate the slope m.
m+=+%282600-3500%29%2F%28250-25%29
m+=+-900%2F225
m+=+-4
A negative slope makes sense since the bullet is slowing down as the distance increases.
So we have m, let's plug that in
S%28t%29+=+S%280%29+-+4%2AD%28t%29
Now use either one of the given data points and plug that in. Then solve for S(0)
3500+=+S%280%29+-+4%2A25
3500+=+S%280%29+-+100
3600+=+S%280%29
So plug that in
S%28t%29+=+3600+-+4%2AD%28t%29
Test that against the two data points we know. Does it yield 3500 at 25 and 2600 at 250? Check it out
Now you know the equation. So use it to solve parts B through D. For B plug in d(t) = 300 and solve for S(t). For C, plug in S(t)=500 and solve foe D(t).
For D, D(t) = 0.
For E, S(t)=0
For F, we already solved for m in the beginning. What does m mean? It gives the rate the speed slows per foot traveled.