I did what you said, and the good news is that I came up with the following equation:
\frac{d^{2}g}{4H - 2h + 4\sqrt{H(H-h)}} = v^{2} - 2gH + 2gh
The bad news is that I need to solve for the initial height, h in terms of all the other variables, and there seems to be no easy way to make...
Suppose you know only these three things about a launched projectile:
- Initial launch velocity (magnitude only, not direction)
- Maximum height reached
- Horizontal distance traveled before hitting the ground
Is it possible to find the initial height, launch angle, and airtime of this...
When the angle canceled out, I was left with an equation whose only unknowns were the total time and velocity. I managed to express t in terms of h_max, h_0, and fundamental constants and solved for v, which could then be used for theta. In response to voko, I didn't see that approach until now...
Thank you so much! I don't think you solve for the velocity in the height equation, only the vertical component. But using your steps, I was able to get the angle to cancel out and get only the velocity. The ugliest kinematics equation I've ever seen, but it gets the job done.
Hi everyone,
I'm trying to design a formula that determines the launch velocity, launch angle, and time spent in the air for a projectile if only the initial launch height, maximum height reached, and total horizontal distance traveled before the projectile hits the ground are known. It's not...