1. A man can swim across a river at a speed of 8 m/s due East, but the river's current is flowing South at 6 m/s, what is his velocity with respect to the bank? a. 10 m/s @ 36.9 N of E b. 10 m/s @ 53.1 S of E c. 10 m/s @ 36.9 S of E d. 10 m/s @ 36.9 E of N 2. A cannon fires a shell at 180 m/s at an angle of 25" to the horizontal. How far does it travel on level ground? (Show your work) 3. Which of the following is an accurate representation of displacement vector in two dimensions? a. R b. C. d. D 4. Explain the component method of solving kinematic problems in more than one dimension. 5. A cannon fires a shell at 100 m/s. If I wish to hit a target 200 m away, what angle should the cannon be positioned? a. 5.65 b. 84.4 c. 22.6 d. 11.3 6. A ball is hit by a batter at 30 above horizontal towards the 2.5 m higher outfield ivy covered wall of Wrigley field in Chicago (Home of the Cubs). If the wall is 107.6 m along the right field foul line, at what speed must he hit the ball to get a home run? a. 54.7 m/s b. 42.4 m/s c. 71.2 m/s d. 35.6 m/s 7. Is this sequence of numbers approximately linear, quadratic, cubic, other? 47.1, 47.3, 47.7, 48.3, 49.1 a. Other b. Cubic c. Linear d. quadratic 8. A man can swim across a river at a speed of 6 m/s due East, but the river's current is flowing North at 3.2 m/s, what is his velocity with respect to the bank? (Show your work) 4. (13 points) About 10 seconds after lift-off, the Space Shuttle undergoes a rolling pullup. Because the orientation of the Space Shuttle at launch results in a singularity when described by a standard 3-2-1 rotation sequence, a 3-1-3 rotation sequence is used instead with angles , 0, and . At the time of observation (about 10 seconds after lift-off), the Space Shuttle has an orientation of = 0 deg, 0 =90, deg, and = -90 deg. In addition, the vehicle is experiencing a roll rate p and a pitch rate q. The mass moment of inertia matrix is given by the following: 1xx 0 0 IB = 0 Lyy 0 0 0 Izz Find an expression for the components of the moment expressed in the body frame required at this point in time to continue the maneuver. [Hint: Use the rotational kinematic equations developed in Problem 1. Note that while angles 0 and (and their time rate of change) from a 3-1-3 rotation sequence do not have the same meaning as those from a 3-2-1 rotation sequence, the components of the angular velocity expressed in the body frame (i.e., p, q, and r) do.]