## Equation with one unknown

### Sigurd Indrehus (view profile)

on 20 Sep 2019
Latest activity Edited by Stephan

on 20 Sep 2019

### Stephan (view profile)

I want to find out at what time a object hits the ground, this is the equation:
2*m/(A*Cd*d)* log(abs(cosh(t*sqrt(A*Cd*d*g/(2*m)))))-1000=0
With following parameters:
g=9.807; %m/s2
d= 1.225; %kg/m3
delta_t=0.01; %arbitrary small number
t=0:delta_t:50; %total time from 0 to 50 (s)
A=1.9;
m=84;
Cd=1.14;
I want to solve this equation for t, which is the only unknown. How do I do this?

### Stephan (view profile)

on 20 Sep 2019
Edited by Stephan

### Stephan (view profile)

on 20 Sep 2019

With Symbolic Toolbox:
syms t positive
g=9.807; %m/s2
d= 1.225; %kg/m3
A=1.9;
m=84;
Cd=1.14;
fun = 2*m/(A*Cd*d)* log(abs(cosh(t*sqrt(A*Cd*d*g/(2*m)))))-1000 == 0
sol = double(solve(fun,t))
Using basic functions:
g=9.807; %m/s2
d= 1.225; %kg/m3
A=1.9;
m=84;
Cd=1.14;
fun = @(t) 2*m/(A*Cd*d)* log(abs(cosh(t*sqrt(A*Cd*d*g/(2*m)))))-1000
sol = fzero(fun,10)