The equation describing the horizontal motion of a particle versus time is given below.

x = ( t³ - 6t² - 15t + 40 ) m

C.1. Plot the x versus t graph over the range t = 0 s to t = 6 s.

C.2. Compute dx/dt

C.3. During what interval(s) is the derivative of the equation negative? positive?  What is the value of dx/dt @ t=2 s?

C.4.  Compute the integral of the equation:  dy/dt = ( 9.81t + 1.2 ) m/s

C.5.  What was the change in value of y between t=1 s and t=4s?

C.6.  If the value of y at t=1 s was 0.5 m, what is the value of y at t=4s?

Listed below are three vectors that point from the origin of a right-handed orthogonal three-dimensional reference frame to the shoulder (V1 ), elbow (V2 ) and wrist (V3 ), respectively, of the throwing arm of a baseball pitcher. Note, i and j are unit vectors in the horizontal directions (j points towards home plate and i is perpendicular to j and points towards third base), and k is a unit vector pointing in the vertical direction.

V1 = (10.02 i + 11.08 j + 1.10 k ) m

V2 = (10.19 i + 11.33 j + 1.22 k ) m

V3 = (10.27 i + 11.55 j + 1.36 k ) m

Plot the following views of these three vectors on graph paper. Use a scale that will allow you to easily visualize the vectors and keep the same relative scale for all axes (e.g., X: 10.00 to 10.60;Y: 11.00 to 11.60; Z: 1.00 to 1.60)

V.1. Graph A: Z versus X. This will be a back view.

V.2. Graph B: Z versus Y. This will be a side view.

V.3. Graph C: Y versus X. This will be an overhead view.

When you create a graph of B versus A, B is plotted on the vertical axis or ordinate and A is plotted on the horizontal axis or the abscissa

From the data compute the following measures:

V.4. UA , a vector that points from the elbow to the shoulder.

V.5. FA , a vector that points from the elbow to the wrist.

V.6. Plot (or sketch) UA and FA on

a. Graph A 

b. Graph B 

c. Graph C

V.7. The length of the upper arm (shoulder to elbow).

V.8. The length of the forearm (elbow to wrist).

V.9 UA * FA (Asterisk is used to indicate the dot product symbol in the web browser)

V.10 The elbow angle in degrees.