Two Dimensional Motion and Vectors

Vector Basics

1

A quantity that indicates both a magnitude and a direction

Vector

2

A quantity that only indicates a magnitude, not a direction

Scalar

3

What is the scalar quantity of velocity?

Speed

3

In projectile motion calculations, this is the only scalar quantity, meaning it can be used in the calculations of motion in both component directions

What is Time?

3

A vector that represents the sum of two or more vectors

Resultant vector

3

Give three examples of a scalar quantity and three examples of a vector quantity.

Scalar: mass, volume, distance, speed, etc Vector: velocity, acceleration, force, displacement, etc

Vector Operations

1

How are vectors added graphically?

Head to Tail?

2

A plane flies 45 km east and then 70 km north. What is the magnitude and direction of its displacement?

83.2 km at 57.2 degrees north of east

3

A bird flies 14 km west and then 25 km south. What is the magnitude and direction of his displacement?

28.6 km at 60.75 degrees south of west.

3

How do you go about adding 2D Vectors?

Divide each vector into it's components.  Perform the calculations with the components independently. 

If necessary, combine the components of the resultant to determine the magnitude and direction of the resultant. 

3

Ms. Collins flies at a velocity of 45 km/h at 30 degrees north of east. What are the horizontal and vertical components of her velocity?

22.5 km/h north 38.9 km/h east

3

Ms. Collins is running outside. She runs 3.0 miles to the north, 1.0 miles to the east, and then 1.5 miles to the south. What is the total distance that she traveled? What is the magnitude and direction of her displacement?

Total distance traveled= 5.5 miles Displacement= 1.80 miles at 33.69 degrees east of north

Adding Non-Perpendicular Vectors

1

How are 2D vectors added algebraically?

Break vectors into components.  Perform the vector addition component by component. (Keeping in mind same direction same sign. Opposite direction opposite sign) 

Find the components of the resultant. 

2

A football player runs directly down the field (horizontally) for 35 meters before turning to 25 degrees above the horizontal and running an additional 15 meters before being tackled. What is the magnitude and direction of his total displacement?

49.00 m at 25.01 degrees above the horizontal

3

A plane travels 2.5 km at 35 degrees above the horizontal and then changes direction and travels 5.2 km at 22 above the horizontal. What is the magnitude and direction of his displacement?

7.65 km at 26.13 degrees above the horizontal

3

During a rodeo, a clown runs 8.0 m north, turns 55 degrees north of east, and runs 3.5 m. Then, after waiting for the bull to come near him, the clown turns due east and runs 5.0 m out of the arena. What is the magnitude and direction of the clown's displacement?

13.0 m at 57.18 degrees above east of north

3

A bullet traveling 850 m ricochets from a rock. The bullet travels another 640 m, but at an angle of 36° from its previous forward motion. What is the resultant displacement of the bullet?

What is 1420m at 16 degrees?

3

Hurricane Iniki moved for 790 km at an angle of 18° north of west, then moved due west for 150 km, turned north and continued for 470 km, and finally turned back 15° east of north and moved 240 km to cross the island of Kauai. What was the resultant displacement of Hurricane Iniki?

What is 1260km at 48 NoW?

Projectile Motion

1

Describe the horizontal velocity of a projectile

constant

2

Describe the vertical acceleration of a projectile

constant and negative (usually -9.81 m/s2)

3

Describe the vertical acceleration of a projectile

zero

3

What does the time of flight for a projectile depend on?

The vertical components of velocity, displacement, and acceleration. 

3

For a projectile launched from the ground and landing back on the ground, what can be said about its initial and final vertical velocities?

Same magnitudes, different directions (one is positive and one is negative)

3

What can be said about the vertical velocity of a projectile at the top of its path?

Zero

Projectiles Problem Solving Practice

1

Draw a diagram to represent the projectile motion. Label initial and final velocity, trace the trajectory. 

A ball is launched at an angle of 37 degrees above the horizontal at a speed of 40m/s from the top of a building that is 20m high. 

2

A bridge rises 321 m above a river. If a rock is kicked horizontally off a bridge to land 45.0 m from the base of the bridge, what is the speed at which the rock was kicked?

5.56 m/s

3

People in movies often jump from buildings into pools. If a person jumps horizontally from the 10th floor (30 m high) to a pool that is 5.0 m away from the building, with what initial speed must the person jump?

2.02 m/s

3

A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper.

TOF= 1.15 s x= 12.16 m y=1.61 m

3

Salmon often jump waterfalls to reach their breeding grounds. One salmon starts 2.00 m from a waterfall that is 0.55 m tall and jumps at an angle of 32.0 degrees. What must be the salmon's minimum speed to reach the waterfall?

6.87 m/s

3

A cannon is fired with an initial velocity of 25.0 m/s at 15 degrees above the horizontal. If the cannon is on a cliff that is 40 meters high, how long is the cannon ball in the air for? How far away from the base of the cliff will the ball land?

What is 3.59s and 86.69m?