Q1. A metal block of mass m slides on a horizontal surface that has been lubricated with a heavy oil so that the block suffers a viscous resistance that varies as the 3/2 power of the speed F(v)=-cv^3/2. If the initial speed of the block is v0 at x=0, show that the block cannot travel farther than 2mv0^1/2 / c.

Q2. On a spacecraft two engines fire for a time of 396s. One gives the craft an acceleration in the x direction of ax = 9.04 m/s2, as other produces an acceleration in the y direction of ay = 7.7m/s2. At the end of the firing period, craft has velocity components of vx = 4430 m/s and vy = 3950 m/s. Find out the magnitude and direction of initial velocity. Express the direction as an angle with respect to the +x axis.