How do I fix this equation?
r= v^2/(g)tan( )
well, you need an angle. How you fix it depends on what you want it to do.
If it has anything to do with a trajectory, you might want to read the excellent article in wikipedia.
I am not sure what you mean.
Perhaps it has something to do with how high a projectile goes
kinetic energy due to vertical velocity component at ground = potential energy at top
(1/2) m v^2 = m g h
so
h = v^2/ (2g)
now if you launched at angle T from the ground at speed s
then v = s sin T
and u = horizontal component of speed = s cos T
now how long did it take to reach that height h?
average speed up = v/2
so time going up = 2 h /v
the total time in the air including the fall is then 4 h/v = 4 v^2/(2gv) = 2v/g
so how far did it go along the ground, range r?
time times horizontal component of speed = Time in air * s cosT
r= 2 v/g * s cos T
but v = s sin T
r= (2/g)s^2 sin T cos T = (s^2/g) sin 2T
I derived this equation from Banking of Curves without friction which is:
mgtan( )=mv^2/r
The problem was asking for the radius which r, so I came up with the formula:
r=v^2/gtan()
I do not know how the rules of inverse apply to the derivation of the formula.
All other variables are given which are:
v= 15 m/s
g(ravity)=9.8 m/s^2
Angle= 20 degrees (tan(20))
oh
call force normal to track = F
horizontal force = m v^2/R = F sin 20
vertical force = m g = F cos 20
so
F= m v^2 /R sin 20 = m g/cos 20
g R sin 20 = v^2 cos 20
R = (v^2/g ) cos 20/sin 20 = v^2/ (g tan 20)
To fix the equation, we need to specify the value inside the tangent (tan) function. The equation you provided is: r = v^2/(g)tan( ).
Here's how you can fix it:
1. Determine the value that needs to be plugged into the tangent function. It could be an angle in degrees (°) or radians (rad). Let's assume it's an angle in degrees, and we'll call it θ.
2. Replace the empty space inside the tangent function with the symbol representing the angle you want to use. The modified equation would be: r = v^2/(g)tan(θ).
Keep in mind that you'll need to provide a specific value for θ in order to accurately solve the equation. Once you have a number for θ, you can plug in the values of v, g, and θ to compute the value of r.