SOLUTION: I just don't know how to set this problem up. I need help! Ely stands next to his cousin Teri. He shoots his bb-gun at a straight horizontal angle. Teri records the time it tak

Question 149102: I just don't know how to set this problem up. I need help!
Ely stands next to his cousin Teri. He shoots his bb-gun at a straight horizontal angle. Teri records the time it takes from the moment Ely fires the bb-gun until the sounds of the ping(the bb hitting the can) to return, .25 seconds. The distance is 20 yards. The speed of sound is 1140 ft per sec. How fast does the bb travel? Hos far did the bb fall? The equation he gave us h=-16t^2+vt+h
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I'm just going to give you a few hints to start with. You can write back if you are still having problems.

The BB has to hit the target to make the sound, so the sound doesn't start moving toward your ear until the BB has travelled from the muzzle of the gun to the target. You know the distance, 20 yards, and the speed of sound (1140 ft/sec). First hint, convert 20 yards to the equivalent number of feet. Then using d = rt in the form of t = d/r, you can calculate the time it took for the sound to return from the target. Subtract that from .25 seconds and you will have the time it took the BB to travel from the gun muzzle to the target. Again, using d = rt this time in the form r = d/t, you can calculate the rate of speed of the BB.

The second part of the question is sort of tricky. You are given the instantaneous height formula: , where is the height of the projectile at time , in other words the initial height of the BB or height of the muzzle of the gun above the ground. This won't matter much, and you can leave it as a variable, as long as Ely is a normal-sized human being and is standing upright when he fires the BB gun -- the BB won't fall enough in 20 yards to matter. (If Ely is a 12-inch tall space alien, all bets are off)

But the really tricky part of this is to realize that the in your function is the initial VERTICAL velocity. It has nothing whatever to do with the velocity of the projectile as it exits the gun since the gun was fired with the muzzle perfectly horizontal meaning that there is no vertical component to the velocity of the BB imparted by the gun. The only force acting vertically on the BB is gravity. In fact, if you dropped a BB from the level of the gun muzzle at the same instant that you fired one, they would hit the ground at the same time. Therefore, , and ( being the time of flight you calculated doing the first part of the problem) gives you the amount to subtract from the initial height , in other words, the distance that the BB drops by the time it hits the target.
RELATED QUESTIONS
I just don't know how to set this problem up. I need help! Ely stands next to his... (answered by ankor@dixie-net.com)

Here is the problem. Time Traveled on a Visit. Steve leaves Nashville to visit his... (answered by solver91311)

I just need to know how I would set up this equation. the Question is A company makes tv... (answered by rfer)

If Don subtracts 24 from one-half of his number he gets 0. What is Don's number? I... (answered by blwinbbbles,stanbon)

Please help with this problem< i am terrible at math an i just don"t get it?? I even... (answered by stanbon)

I need help on this problem: A 50 meter dash runner starts at the gun and reaches the... (answered by josmiceli)

Find the interest on $2500 invested for 5 years at 10% compounded quarterly. I know... (answered by rfer)

Need help, I think I know the answer but not sure. George puts his canoe in at St. Louis. (answered by Paul)

Mr. Jones is selling his boat for $6,870. He has received two offers: one buyer agrees to (answered by ankor@dixie-net.com)