- #1

cojaro

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**1. "A projectile is fired with a velocity**

**u**at the entrance*A*of a horizontal tunnel of length*L*and height*H*. Determine the minimum value of*u*and the corresponding angle [itex] \theta [/itex] for which the projectile will reach*B*at the other end of the tunnel without touching the top of the tunnel."[itex]

\begin{center}

v_0 = u\\

x = L , x_0 = 0\\

y = H , y_0 = 0\\

\end{center}

[/itex]

The book gives the answer as http://latex.sidoh.org/?render=%24u%20%3D%20%5Csqrt%7B2gH%7D%20%5Csqrt%7B1%20%2B%20%5Cleft%28%20%5Cdfrac%7BL%7D%7B4H%7D%20%5Cright%29%5E2%24 and http://latex.sidoh.org/?render=%24%20%5Ctheta%20%3D%20%5Ctan%5E%7B-1%7D%5Cleft%28%7B%5Cdfrac%7B4H%7D%7BL%7D%7D%5Cright%29%24

## Homework Equations

http://latex.sidoh.org/?render=%5Cbegin%7Bcenter%7D%0D%0A%24v_%7Bx_0%7D%3Du%5Ccos%7B%5Ctheta%7D%3Dv_x%24%20%5C%5C%0D%0A%24v_%7By_0%7D%3Du%5Csin%7B%5Ctheta%7D%24%20%5C%5C%0D%0A%24x%3Dut%5Ccos%7B%5Ctheta%7D%24%20%5C%5C%0D%0A%24y%3D-%5Cfrac%7B1%7D%7B2%7Dgt%5E2%2But%5Csin%7B%5Ctheta%7D%2By_0%24%20%5C%5C%0D%0A%24v_y%3D-gt%2Bu%5Csin%7B%5Ctheta%7D%24%20%5C%5C%0D%0A%5Cend%7Bcenter%7D

## The Attempt at a Solution

So, I asked my teacher to set it up for me. I've wrapped my head around this for the past week and just don't see it! I've tried so many danged angles of approach and still get nowhere. My teacher's setup didn't help me much, either, so there's not much work-out to do. My teacher left me with four equations:

http://latex.sidoh.org/?render=%5Cbegin%7Bcenter%7D%0D%0A%5Cbegin%7Bequation%2A%7D%0D%0Ax%20%3D%20%5Cdfrac%7BL%7D%7B2%7D%20%3D%20u%20%5Ccos%7B%5Ctheta%7D%28%20%5Cfrac%7Bt_f%7D%7B2%7D%29%0D%0A%5Cend%7Bequation%7D%0D%0A%5Cbegin%7Bequation%2A%7D%0D%0AL%20%3D%20u%20t_f%20%5Ccos%7B%5Ctheta%7D%0D%0A%5Cend%7Bequation%7D%0D%0A%5Cbegin%7Bequation%2A%7D%0D%0AH%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%20g%20%5Cleft%28%5Cfrac%7Bt_f%7D%7B2%7D%5Cright%29%5E2%20%2B%20u%20%5Csin%7B%5Ctheta%7D%28%20%5Cfrac%7Bt_f%7D%7B2%7D%29%0D%0A%5Cend%7Bequation%7D%0D%0A%5Cbegin%7Bequation%2A%7D%0D%0A0%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%20g%20t_f%5E2%20%2B%20u%20t_f%5Csin%7B%5Ctheta%7D%0D%0A%5Cend%7Bequation%7D%0D%0A%0D%0A%5Cend%7Bcenter%7D

with [itex]t_f[/itex] being the time to get to B. He told me to plug'n'play and that I'd eventually get the answer.

(I also had some troubles writing latex using the [ latex] XXX [ \latex ] HTML things. It kept messing up, misaligned and showing the variables as text, not math text, namely, v versus [itex] v [/itex]. )

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