A ball is thrown vertically upward

A ball is thrown vertically upward with an initial velocity of $v_0=10$ m/s. There is a velocity dependent drag force directed in the opposite direction to the velocity. The total force on the ball is gravity plus the drag force $F=-mg-bv_x$, where $F$ is the force, $m$ is the mass of the ball, $g=9.81$ m/s² is the acceleration of gravity at the earth's surface, $b$ is the drag force constant, and $v_x$ is the velocity. The acceleration of the ball is $a_x=-g-bv_x/m$. The motion is in a line which we can take to be the $x$-axis. The equations are loaded into the numerical second order differential equation solver below.

$m=$ 1 [kg]

$b=$ 0.4 [kg/s]

For long times, the ball falls with a constant terminal velocity $v_{\text{terminal}}=-mg/b=$ -24.5 m/s.

 Numerical 2nd order differential equation solver 

$ \large \frac{dx}{dt}=$

$v_x$

$ \large a_x=\frac{F_x}{m}=\frac{dv_x}{dt}=$

Intitial conditions: 

$x(t_0)=$

 

$\Delta t=$

$v_x(t_0)=$

 

$N_{steps}$

$t_0=$

 

Plot:

vs.

 

 $t$       $x$      $v_x$