Calculating Initial Speed of a Projectile Using Gravity, Height, and Range

AI Thread Summary
The discussion focuses on calculating the initial speed of a projectile using gravity, height, and range. Participants share a formula they derived: Initial Velocity = sqrt((1/2 * g * R^2)/(cos2θ * (R * tanθ + H)). Despite extensive collaboration and research, they struggled to find relevant resources online. After three hours of calculations, they successfully arrived at the final answer. The collaborative effort highlights the challenges of solving projectile motion problems in physics.
nobodyuknow
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Homework Statement



Find the initial speed (Vo) in Projectile motion in terms of
Gravity (g)
Height (H)
Range (R)

Homework Equations



Nothing has been given, however, have found these so far...

Initial Velocity = sqrt((1/2 * g * R^2)/(cos2θ * (R * tanθ + H))

And a few others which are irrelevant.

The Attempt at a Solution



My friends and I are all collaborating and the above formula is the closest thing we've come up with.
We've also resorted to looking up on Google and Yahoo answers without much luck. Similar questions have aroused on Physics Forums, but not quite what we're after.
Thanks :)
 
Last edited:
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After literally, 3 hours of arithmetic. We got the final answer.
 
Last edited:
Hey,
Your answer is perfect :-)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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