Equation with one unknown

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?

Answer 1

[Stephan]

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)