FIRST ORDER LINEAR EQUATIONS TO DYNAMICS A rocket that starts from rest is propelled by a constant thrust of 3000 pounds in a straight horizontal path for 40 seconds. Suppose that, as the propellant is burned, the mass of the rocket varies with time in accordance with m = 50 – t slugs, and that the drag force is numerically equal to four times the velocity. Please answer both parts: a) Find the velocity equation of the rocket (which includes finding C) b) What is the velocity of the rocket when t = 30 seconds?

Pitch direction A baseball pitcher throws a curveball by spinning and throwing the ball, and the schematic diagram shows the stylized pattem of air flow around the ball on a horizontal plane. As the ball travels in the air, it also spins, causing the air flow velocity on the right of the ball, Vz, to be lower than the air flow velocity on the left, VL. The air has density, p. Air flow around the ball p-12 kg/m VR 15 m/s V 18 m/s g-9.81 m/s Spin direction (a) Which way will the baseball curve? To the left, or to the right? (b) Use Bernoulli's cquation to estimate the magnitude of pressure difference between the left and right sides of the ball, that causes the ball to curve. VL VR