# Math Help - mathematics mechanics help

1. ## mathematics mechanics help

yutyy

2. Originally Posted by longy
A ball is projected vertically upwards with an initial speed of 30ms^-1 the time taken for the ball to reach its maximum height is 3 s and the maximum height that the ball reaches is 30m.The remainder of the question we revise by taking air resistance in to account.Model the the ball as a shpere of radius D,mass m,and assuming that the quadratic model of air resistance applies.My question is i need to show that the acceleration at time t is a(t)i in which a(t)=-g/b^2(v(t)2+b^2) where v(t)i is the velocity of the ball at time t,and b^2=mg/0.3D^2 I f somebody could help me or give me a few tips thanks.
The equation of motion will be given by the differential equation
$ma = mg - kv^2$

I would call the quadratic resistance coefficient b, but the units for it are all wrong. You'll have to figure out what to do with that yourself.

So
$\frac{dv}{dt} = g - \left ( \frac{k}{m} \right )v^2$

Solve for v.

-Dan