Answer:
See below for answers and explanations (along with a graph for #3)
Step-by-step explanation:
<u>Problem #1</u>
Applying scalar multiplication, .
Its magnitude would be .
Its direction would be .
Thus, B) 816; 62° is the correct answer
<u>Problem #2</u>
Find the time it takes for the ball to cover 13ft:
Find the height of the ball at the time it takes for the ball to cover 13ft:
Thus, A) 10.053 is the correct answer
<u>Problem #3</u>
We have and as our vectors. Thus, . Attached below is the correct graph. You can also solve the problem visually by using the parallelogram method where the resultant vector is the diagonal of the parallelogram.
<u>Problem 4 (#7)</u>
<u />
Thus, C) -46 is the correct answer
<u>Problem 5 (#8)</u>
Find and :
Find the true direction angle accounting for Quadrant IV:
Write the complex number in polar/trigonometric form:
Thus, C) 8.246(cos 284.036° + i sin 284.036°) is the correct answer
<u>Problem 6 (#12)</u>
Eliminate the parameter and find the rectangular equation:
Thus, D) x^2-9y+45=0 is the correct answer
<u>Problem 7 (#13)</u>
Find the magnitude of the vector:
Find the true direction of the vector accounting for Quadrant II:
Write the vector in trigonometric form:
Thus, D) w=85cos155°i+85sin155°j is the corrwect answer
<u>Problem 8 (#15)</u>
Thus, C) (-3,-13) is the correct answer
<u>Problem 9 (#16)</u>
Treat the golf ball and wind as vectors:
<-- Golf Ball
<-- Wind
Add the vectors:
Find the magnitude of the resultant vector:
Find the true direction of the resultant vector accounting for Quadrant II:
Thus, B) 1.769 m/s; 97° is the correct answer
<u>Problem 10 (#17)</u>
Identify the vectors and add them:
Find the magnitude of the resultant vector:
Find the true direction of the resultant vector accounting for Quadrant IV:
Thus, A) 53.241, 355° is the correct answer
<u>Problem 11 (#18)</u>
We observe that and , hence,
Thus, Q is the correct answer
<u>Problem 12 (#19)</u>
Find the dot product of the vectors:
Find the magnitude of each vector:
Find the angle between the two vectors:
Thus, C) 49° is the correct answer
<u>Problem 13 (#20)</u>
Using scalar multiplication,
Thus, A) -80i - 29j is the correct answer