___________________ Simplify 2 sin(θ) cos(θ) Write only the first result.
___________________ Simplify (1 − cos²θ)(1 − cot²θ) Write only the first result.
_________ The equation for a projectile is given by:
For a velocity v of 14 m/s, and an angle of 30°, calculate the distance d.
_________ Solve for the velocity v:
with the angles given in degrees.
_________ Solve for the angle x: 19.6 sin(x) cos(x) = 9.8
Report the angle x in radians for the solution between 0 and π/2.
(_______, _______) For my physical science test I needed to move an electron at position a to position b. Note that in this example (0, 0) is at the center of the circle. Position a is (170,0). See the diagram on the below left. What are the coordinates of electron b?
____________ Calculate the magnitude (vector length) for the vector {80, 80}. Note that in the diagram on the above right all vectors are in the standard position with their initial point at the origin (0, 0).
____________ Calculate the angle relative to the horizontal axis for the vector {80, 80}.
____________ Calculate the magnitude for the vector {−86.61, 50}.
____________ Calculate the angle relative to the horizontal axis for the vector {−86.61, 50}.
____________ Calculate the magnitude for the vector {−40, −30}.
____________ Calculate the angle relative to the horizontal axis for the vector {−40, −30}.
____________ Calculate the magnitude for the vector {95, 0}.
____________ Calculate the angle relative to the horizontal axis for the vector {95, 0}.
On a Thursday evening in July 2005 I was body board surfing in Malem. My total
velocity v (speed) was the result of the vector addition of the
velocity (speed) of the wave w and the velocity s of my board
along the face of the wave. On that Thursday the waves were moving at a speed of:
m/s due East towards Malem and my board was moving at
m/s due North towards Lelu.
Note that w and s are at right angles as shown in the inset diagram.
Calculate my velocity v over the reef: __________
_________ Calculate the angle between v and w.
Children body boarding in the surf off of Piyuul, Malem.