SOLUTION: 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.

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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.

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52875) About Me  (Show Source):
You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~ 

They want you express "v" via other variables, using the given formula.


From  T = 7000%2A%28w%2Fd%5E2%29%2A%281%2Fv-1%2Fu%29,  you have, step by step


      1%2Fv - 1%2Fu = T%2F%28%287000%2A%28w%2Fd%5E2%29%29%29,

      1%2Fv - 1%2Fu = %28T%2Ad%5E2%29%2F%287000%2Aw%29

      1%2Fv = %28T%2Ad%5E2%29%2F%287000%2Aw%29 + 1%2Fu

      v   = 1%2F%28%28T%2Ad%5E2%29%2F%287000%2Aw%29+%2B+1%2Fu%29%29.          (1)


      v   = %287000%2Aw%2Au%29%2F%28T%2Ad%5E2%2Au+%2B+7000%2Aw%29.       (2)


It is just the formulas to use.  You may use any of these two formulas, (1) or (2), on your choice.

That's it.



Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

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.


matrix%281%2C3%2C+Td%5E2uv%2C+%22=%22%2C+%227%2C000%22wu+-+%227%2C000%22wv%29 ---- Cross-multiplying
matrix%281%2C3%2C+Td%5E2uv+%2B+%227%2C000%22wv%2C+%22=%22%2C+%227%2C000%22wu%29 ---- Adding 7,000wv to both sides
matrix%281%2C3%2C+v%28Td%5E2u+%2B+%227%2C000%22w%29%2C+%22=%22%2C+%227%2C000%22wu%29 ---- Factoring out v on left side

 ----- Dividing both sides by Td%5E2u+%2B+%227%2C000%22w to get the value of v (velocity), in 
                                         terms of d (diameter), T (time, in seconds), u (muzzle velocity), and w (weight).