Science:Math Exam Resources/Courses/MATH102/December 2019/Question 11/Solution 1

We use separation of variables to solving the first order differential equation

${\begin{aligned}{\frac {dv}{dt}}&=-10-v\\{\frac {dv}{10+v}}&=-dt\\v(t)&=ce^{-t}-10\\\end{aligned}}$

Since the initial velocity is v(0) = 10, we have the constant c = 20.

When it reaches the peak of its arc, the velocity is 0. Thus solving for

$v(t)=20e^{-t}-10=0,\implies t=-\ln({\frac {1}{2}})$