1) A ball is falling through the air and experiences air resistance. It’s velocity in metres per second at time t is given by dx/dt=250(e^(-0.2t) -1) where x is the height above the ground.

What is it’s eventual speed?

2) A tap on a large tank is gradually turned off so as not to exact any hydraulic shock. As a consequence, the flow rate while the tap is being turned off is given by dV/dt= -2+0.1tm^3/s.

I worked out the function to be V=-2t+1/20t^2+520.

The question is suppose that it is necessary to let out a total of 300m^3 from the tank. How long should the tap be left fully on before gradually turning it off?

3) over spring and summer the snow and ice on a mountain is melting at a rate of dI/dt = -5+4cos Pi/12 t where t is the time in days and I is the tonnage of ice.
A) Explain from the given rate why this ice is always melting?
B) The beginning of the next snow season is expected to be four months away (120 days) show that there will still be snow left on the mountain then. I worked out The function to be I= 18 000 -5t+48/pi sin Pi/12t