# constant velocity.

Show all work. Draw diagrams and explain answers as needed. Partial credit is available.

1) Falling objects subject to aerodynamic drag accelerate initially but then reach what is called a terminal velocity. The motion from this point on is at constant velocity. Consider the motion of an object that has reached a terminal velocity of 28.6 m/s (down) at a height of 230m. If x=0 (the origin) is at ground level and “up” is the positive direction:

a) Write out xf =xi + vit for this motion leaving x and t as variables. The data given represents the t = 0 motion state.

b) **Use the equation formulated in part (a) **to determine the t value at which the object is 50 m high, and the t value at which the object hits the ground.

2) Three students formulate equations to solve the following problem. A lunar lander is making its descent to Moon Base I. The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is 5.0 m above the surface and has a downward speed of 0.8 m/s. With the engine off, the lander is in free fall.

Each uses a different coordinate system to describe the motion depicted in the problem statement and formulates both a position, y, and a velocity v, equation.

Student 1: y = (0.8 m/s)t + 1/2gt2, v = (0.8 m/s) + gt

Student 2: y = 5.0 m – (0.8 m/s)t – 1/2gt2, v = -(0.8 m/s) – gt

Student 3: y = – (0.8 m/s)t – 1/2gt2, v = -(0.8 m/s) – gt

The equations are based on the general forms:

*y *= *yi* + vit+ 1/2at2 and

*v *= *vi* + *at *. And all three formulations are “correct”. In each equation g=+1.6 m/s2 and the initial conditions (t=0) describe the lander 5.0 m from the surface moving downward at 0.8 m/s.

a) In formulating his or her two equations each student had to choose a real world position of the origin (the position of y=0) relative to the lunar surface, and a real world direction at which the y axis points (either up or down). Draw a diagram for each formulation showing the position of the origin relative to the lunar surface and the real world direction at which the y axis points. Briefly explain your reasoning in each case.