MS 101 Alg & Trig test six • 11 July 2014 Name:

Wave equation in terms of wavelength λ and distance x: $y=\mathrm{a}sin\left(\frac{2\mathrm{\pi }x}{\mathrm{\lambda }}\right)$
Wave equation in terms of period τ and time t: $y=\mathrm{a}sin\left(\frac{2\mathrm{\pi }t}{\mathrm{\tau }}\right)$
Period τ and frequency f relationship: $\mathrm{\tau }=\frac{1}{f}$

1. A RipStik was swizzled across a large sheet of paper. Use the wave and wave data provided to answer the following questions.
   
   1. ________ How many waves are shown?
   2. λ = _______________ Write the wavelength λ
   3. a = _______________ Write the amplitude a.
   4. τ = _______________ Write the period τ.
   5. f = _______________ Calculate the frequency f.
   6. y = ______ sin( _________ x). Write out the equation of the wave in terms of the wavelength λ and distance x.
2. Use a spreadsheet to graph the data in the table.

   x	y
   0	0
   1	14
   2	20
   3	14
   4	0
   5	-14
   6	-20
   7	-14
   8	0
   9	14
   10	20
   11	14
   12	0
   13	-14
   14	-20
   15	-14
   16	0
   17	14
   18	20
   19	14
   20	0

   1. ________ How many waves are shown in the spreadsheet graph?
   2. λ = _______________ Determine the wavelength λ
   3. a = _______________ Determine the amplitude a.
   4. y = ______ sin( _________ x). Write out the equation of the wave in terms of the wavelength λ
3. Solve 4 tan(x) −1 = 0 for x in degrees
4. Solve 4(cos x)² −1 = 0 for x in degrees
5. Given the equation for velocity, the launch angle θ, and the distance:
   $\text{distance d}=\frac{2v^2\sin \left(\text{θ}\right)\cos \left(\text{θ}\right)}{\mathrm{9.8}}$
   for a launch velocity v = 15 m/s at θ = 72°
   
   1. v_x = ______________ Calculate the horizontal velocity v_x
   2. v_y = ______________ Calculate the vertical velocity v_y
   3. d = _____________Calculate the distance d the object will travel.
6. For the vector $\stackrel{\rightharpoonup }{u}$ = 260 i + 150 j
   1. magnitude = __________ Calculate the magnitude.
   2. θ = __________ Calculate the direction angle in degrees.
7. A vector with a magnitude of 100 is at a direction angle of 67° to the horizontal. Write the vector in i, j component form.
   
   $\stackrel{\rightharpoonup }{v}$ = ________ i + ________ j
8. Sketch a graph of the following function: $y=40sin\left(\frac{20\mathrm{\pi }x}{12}\right)$
   
9. 1. ____________ The force vector for Jaeger Striker Eureka's right lead helicopter is given by $\stackrel{\rightharpoonup }{F}$ = -120i + 140j. Calculate the angle to the vertical θ in degrees.
   2. ____________ Calculate the magnitude of the vector $\stackrel{\rightharpoonup }{F}$ = -120i + 140j.
10. A force F of 5774 Newtons is being exerted at an angle of 30° to the horizontal on an object.
    1. F ⋅ d ___________ Calculate the energy (work) done to move the object 10 meters using the dot product.
    2. F ⨯ d ___________ Calculate the torque on the object if the lever arm distance is 0.3 meters using the cross product.
11. Given a matrix $A=\left[\begin{array}{cc}3& -5\\ -7& 1\end{array}\right]$ and a matrix $B=\left[\begin{array}{cc}-3& 5\\ 7& -1\end{array}\right]$
    1. Write the matrix A + B
    2. Write the matrix A − B
    3. Write the matrix 2A