Question 1197770

Using the following formula:

T = 7000 w/d^2 (1/v - 1/u)

A projectile of weight w lbs. and diameter d in., with muzzle velocity of u ft.

Determine velocity v, after T sec.

Unsure how to solve.
<pre>{{{matrix(1,7, T, "=", "7,000"(w/d^2) (1/v - 1/u), highlight("====>"), T, "=", (("7,000"w)/d^2)(1/v - 1/u))}}}
{{{matrix(2,3, T, "=", ("7,000"w/d^2)((u - v)/uv), T, "=", (("7,000"w)(u - v))/(d^2uv))}}}
{{{matrix(1,3, Td^2uv, "=", "7,000"wu - "7,000"wv)}}} ---- Cross-multiplying
{{{matrix(1,3, Td^2uv + "7,000"wv, "=", "7,000"wu)}}} ---- Adding 7,000wv to both sides
{{{matrix(1,3, v(Td^2u + "7,000"w), "=", "7,000"wu)}}} ---- Factoring out v on left side

{{{highlight_green(matrix(1,4, v, "(velocity)", "=", "7,000"wu/(Td^2u + "7,000"w)))}}} ----- Dividing both sides by {{{Td^2u + "7,000"w}}} to get the value of v (velocity), in 
                                         terms of d (diameter), T (time, in seconds), u (muzzle velocity), and w (weight).</pre>