Engineering Dynamics (EngM 373) -- Exam I -- Spring 1996

**Problem # 1:** A projectile is ejected into an experimental fluid at time t=0. The initial speed is *v _{o}* and the angle to the horizontal is q. The drag on the projectile results in an acceleration term

(10 points)

__x-component of velocity:__

Initial conditions:

__x-component of position:__

Initial conditions:

__y-component of velocity:__

Initial conditions:

__y-component of position:__

Initial conditions:

Terminal velocity:

**Problem # 2:** A rocket traveling above the atmosphere at an altitude of 500 km would have a free-fall acceleration *g*= 8.43 m/s^{2} in the absence of forces other than gravitational attraction. Because of thrust, however, the rocket has an additional acceleration component a_{1} of 8.8 m/s^{2} tangent to its trajectory, which makes an angle of 30^{o} with the vertical at the instant considered. If the velocity *v *of the rocket is 30000 km/h at this position, compute the radius of curvature of the trajectory and the rate at which *v* changes with time.

(10 points)

**Problem # 3:** Collar *A* and *B* slide along the fixed rods and are connected by a cord of length *L*. If collar *A* has a velocity to the right, express the velocity of *B *in terms of *x*, *v _{A}*, and

(10 points)

**For extra credit:** If a point *P* is moving in the plane *z=0*, then , thus . Why then isn't .

(3 points)

**For extra credit:** show that for a vector ** b** if |

(3 points)