CHAPTER 3 - VECTORS AND PROJECTILES

Question 1

Vectors have both _____ and _____

Answer 1

magnitude and direction

Question 2

Describe magnitude and direction.

Answer 2

Magnitude answers “how much?” and direction answers “which way?”

Question 3

What is difference between vector and scalar quantities?

Answer 3

Vectors have magnitude and direction, so combining them is tricky. Scalars have magnitude only, so they can be easily added, subtracted, multiplied and divided.

Question 4

Give examples of vector quantities.

Answer 4

Velocity, acceleration, and force.

Question 5

Give examples of scalar quantities.

Answer 5

mass, time, volume, area.

Question 6

A thrown baseball has has two velocity components. Describe them

Answer 6

A vertical component and a horizontal component. The vertical component and the horizontal components are independent, so they do not act on eachother.

Question 7

Discuss the vertical component of a thrown baseball

Answer 7

The vertical component is impacted by gravity, so always changing by 10m/s per second. It changes the same as something thrown straight up in the air.

Question 8

Discuss the horizontal component of a thrown baseball.

Answer 8

Because we ignore air resistance, we assume that the baseball moves at constant velocity horizontally.

Question 9

For projectiles, how can we think of the horizontal and vertical speeds? (shadows)

Answer 9

We can imagine SHADOWS. For Vx, or the horizontal speed, imagine sun above and picture the movement of the shadow of the ball moving on the ground. For Vy, imagine a bright light shining directly behind the motion towards a wall. Now imagine the movement of the shadow of the ball along the wall, that would be the vertical component.

Question 10

If we know the horizontal and vertical component of a thrown baseball, how can we find the initial velocity?

Answer 10

Use the PYTHAGOREAN THEOREM v = sqrt (h squared + v squared)

Question 11

Suppose you know the hypotenuse and the measure of an angle, and want to find the side close to the angle, how do you do it? how do you find the close side?

Answer 11

hypotenuse x COS (angle) [cosine finds the close side]

Question 12

Suppose you know the hypotenuse and the measure of an angle, and want to find the side across from the angle, on the opposite side?

Answer 12

hypotenuse x SIN (angle) [sin finds opposite side]

Question 13

The vector given is usually the ________ of the triangle.

Answer 13

hypotenuse

Question 14

Plane traveling north at 300 km/h hits headwind of 100km/h. What is landspeed? airspeed?

Answer 14

landspeed is 200km/h and airspeed is still 300km/h

Question 15

Special triangles?

Answer 15

3-4-5 (37-53-90), 1-1- sqrt 2 (45-45-90), 1-sqrt 3- 2 (30-60-90)

Question 16

What are the 3-4-5 right triangle angle measures

Answer 16

ABOUT: 37-53-90. across from those sides respectively)

Question 17

what are the angle measures of a 1-1-root 2 triangle?

Answer 17

45 -45- 90 across from those sides respectively)

Question 18

what are the angle measures of the 1- sqrt 3- 2 triangle?

Answer 18

30- 60- 90 (across from those sides respectively)

Question 19

What are the side lengths of the 37-53-90 triangle?

Answer 19

3-4 and 5

Question 20

What are the side lengths of the 45-45-90 triangle?

Answer 20

1, 1 and sqrt 2

Question 21

What are the side lengths of the 30-60-90 triangle?

Answer 21

1, sqrt 3 and 2

Question 22

A plane traveling north at 300 km/h with no wind: What is landspeed?

Answer 22

landspeed is 300km/h and airspeed is still 300km/h

Question 23

A plane traveling north at 300 km/h airspeed hits southerly wind of 50 km/h. What is landspeed?

Answer 23

250 km/h

Question 24

A plane traveling north at 300 km/h airspeed hits southerly wind of 300 km/h. What is landspeed?

Answer 24

0. It will look like it is standing still in mid-air

Question 25

A plane traveling north at 300 km/h airspeed hits northerly wind of 50 km/h. What is landspeed?

Answer 25

350 km/h. The wind speed adds to groundspeed

Question 26

A plane traveling north at 300 km/h airspeed hits easterly wind of 400 km/h. What is landspeed?

Answer 26

Landspeed is the diagonal of triangle with sides 300 and 400, using 3-4-5 triangle, the diagonal is 500km//h. The airspeed is still 300km/h

Question 27

What is a clever way to look at projectile motion?

Answer 27

Imagining the projectile as a free falling object from different places along a straight diagonal line drawn at initial angle

Question 28

If a bullet is shot horizontally at the exact time another is just dropped from the same height right next to it, which will land first (on flat surface)?

Answer 28

they will land at the same time

Question 29

When drawing velocity vectors along the path of a projectile, what doesn't change?

Answer 29

The horizontal vectors stay the same

Question 30

When drawing velocity vectors along the path of a projectile, how does the vertical vector change?

Answer 30

Gravity impacts it. They become shorter on the way up, and ZERO at top, then get longer on the way down (pointing down) The velocity changes every second (10m/s each second). IT BECOMES ZERO AT THE TOP

Question 31

what is a "horizontal range?"

Answer 31

the distance a projectile travels along the ground (horizontally)

Question 32

What is an interesting fact about horizontal ranges and angles (when kicking a soccer ball or firing an arrow?)

Answer 32

complementary angles (angles that add to 90) have the same horizontal range. EXAMPLE: kicking a ball at 30 degrees will go the same distance as 60 degrees (neglecting air resistance. Shooting an arrow at 10 degrees will travel the same horizontal distance as one shot up at 80 degrees!!!

Question 33

When is a projectile traveling the slowest?

Answer 33

At the top

Question 34

Explain why a projectile is traveling slowest at the top

Answer 34

We know the horizontal component is always the same, so that will always be contributing, but the vertical component becomes ZERO at the top. You can visualize this by imagining a ball thrown straight up.. it stalls at the top for a split second.

Question 35

What angle of elevation maximizes horizontal range?

Answer 35

45 degrees.

Question 36

SATELLITES: How much does the earth curve over 8 km?

Answer 36

about 5 meters

Question 37

SATELLITES: If an object falls at about 5 m in first second, and the earth curves about 5m every 8km. How fast would something have to travel horizontally to never hit the earth?

Answer 37

8km/s (neglecting air resistance)... now you orbit :)

Question 38

SATELLITES: How far up is the international space station?

Answer 38

400 km (250 miles)

Question 39

SATELLITES: How fast does the international space station move?

Answer 39

28,000 km/h about 8 km/s . (17,500 mph, about 5 miles per second)

Question 40

SATELLITES: How many times does the international space station orbit the earth each day?

Answer 40

It circles the earth every 90 minutes, about 16 times a day!!

Question 41

SATELLITES: Why do we have to be above earth's atmosphere to orbit?

Answer 41

Traveling 5 miles in a second, or 8km, air resistance makes it impossible. things would burn up (like shooting stars do)