SOLUTION: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show s

Question 30540: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work
Before GPS and on-board targeting computers, engineers had to figure out how to calibrate optical bomb sites so as to accurately drop bombs on targets. From physics, we know that the altitude of a bomb t seconds after release from a plane flying at an altitude of s0 feet is given by the function s(t) = s0 - 16t2 (disregarding air resistance). We also know that, since d = rt, a bomb released from a plane traveling at r mph itself has a velocity of r mph and will travel rt miles in t seconds (again disregarding air resistance).
a. If a bomb is released at 20,000 feet, how long will it take to strike the ground? (Hint: solve s(t) = 0 for t using s0 = 20,000.)
If R in the diagram is the release point of a bomb relative to the ground, how far should R be from the target to insure a hit, assuming the plane has a velocity of 300 mph?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
s(t)=20,000-16t^2
When the bomb hits the ground its height is zero.
0=20000-16t^2
16t^2=20000
t^2=20000/16=1250
t=35.355 seconds
Cheers,
Stan H.
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