Quiz

QUIZ

1. You are walking 9 blocks east and 5 blocks north. How many blocks do you travel if you are traveling by helicopter in a straight line?

a. 14 blocks b. 17.2 blocks c. 10.3 blocks d. 15.5 blocks

Answer: c. As the answer will be the square root of the squares of 9 and 5, you get 81 plus 25 or 106, of which the square root is 10.3. This is fully based on the Pythagorean theorem.

2. What must be true to use the Pythagorean theorem?

a. The triangle must be on a grid. b. It must be a right triangle. c. All values for the vectors must be positive. d. Vector AB must be greater than vector BC.

Answer: b. The triangle must be a right triangle, with one angle being 90 degrees. According to the theorem, AB2 + BC2 = AC2, in which each of these are vectors and the angle ABC must be 90 degrees in order to have the theorem be valid.

3. You are doing a problem in which an individual travels 9 miles east, 4 miles northwest (at 45 degrees) and 2 miles south. Which vector do you start with in drawing this?

a. 9 miles east b. 4 miles northwest c. 2 miles south d. It does not matter

Answer: d. You can start with any vector you wish because it will result in the same end-result. This problem can be solved on a graph using a head-to-tail vector analysis.

4. You have a vector A and you want to create a vector called -A. What will change in order to make this vector?

a. The magnitude and direction b. The magnitude only c. The direction only d. This is the same vector

Answer: c. In making the vector, you will change the direction to be the reverse of the original vector but the magnitude will be the same. This is the same thing as reversing or “subtracting” the vector.

5. You know the length of the final vector xy and the angle. How do you find the x-component of the vector?

a. The vector is xy times the cosine of the angle theta b. The vector is xy times the sine of the angle theta c. The vector is xy times the tangent of the angle theta d. The vector is xy divided by the tangent of the angle theta

Answer: b. The vector x will be xy times the sine of the angle theta. This can be determined by knowing the magnitude of the final vector xy and its angle and by using a scientific calculator.

6. You know the x and y vectors on a coordinate graph and you want to know the angle of the resultant AB vector. How do you calculate this?

a. The angle is the sine of x times y b. The angle is the cosine of x divided by y c. The angle is the tangent to the negative one of y divided by x d. The angle is the tangent of y divided by x

Answer: c. The angle is the tangent to the negative one of y divided by x. This will require the knowledge of x and y plus a scientific calculator.

7. In the motion of an object, what best defines the placement of the object in space at any particular point in time?

a. Projectile b. Displacement vector c. Gravity d. Trajectory

Answer: b. The displacement vector is the vector that will decide where the object is in space, regardless of its actual trajectory.

8. If you shoot something in the air and determine its velocity at the apex, what will this be with respect to height or the y position?

a. The sine of the angle of the projectile shot b. The cosine of the angle of the projectile shot c. The force of gravity multiplied by the time it takes to reach the apex d. The velocity in the y direction at the apex will be zero

Answer: d. By definition, the velocity at the apex of this kind of projectile being shot in the air will be zero because it is turning around and falling toward the earth because of gravity.

9. You shoot something from a gun to get a range of 20 feet at 80 degrees. What is the range you’ll get if you shoot it at 10 degrees?

a. 200 feet b. 142 feet c. 63 feet d. 20 feet

Answer: d. The same range will be gotten from 80 degrees and 10 degrees because the sum of the two angles is 90 degrees. You can shoot it out of the gun at 80 degrees or 10 degrees and you’ll get the same value for the range.

10. In shooting a projectile, what is the exit velocity?

a. The velocity at which the object goes into orbit around the earth b. The initial velocity of the object as it leaves the gun or cannon c. The velocity of the object at its apex with respect to the y axis d. The velocity of the object at its apex with respect to the x axis

Answer: a. The exit velocity will be the velocity at which the object goes into orbit around the earth.