VECTORS AND

PROJECTILEMOTION

How fast will the plane go if it has a crosswind of

20m/s?

We need to use vectors!!!!!!!

Terms to Know:

• Resultant Vector

• Component Vector X-Component Y-Component

2 Mathematical Tools:• Pythagorean Theorem

a2 + b2 = c2

• SOH-CAH-TOA

hyp

oppsin

hyp

adjcos

adj

opptan

A Trojan walks 45.0 m north, then turns and walks 7.5 m

east. What was the Trojan’s displacement?

(magnitude and direction)

45.6 m at 9.5° east of north

Ebony passes a soccer ball 6.0 m directly across the field to Amber,

who then kicks the ball 14.5 m directly down the field to Duane.

What is the ball’s total displacement?

(magnitude and direction)

15.7 m at 22° from the sideline

Find the component velocities of a helicopter traveling 95 km/hr at an angle of 35° to

the ground.

vx = 78 km/hr ; vy = 54 km/hr

A superhero flies 125 meters down from the top of a tall

building at an angle of 25° below the horizontal. Find the horizontal and vertical

components of his displacement vector.

x = 110. m ; y = -53 m

A truck drives up a hill with a 15° incline. If the truck has a constant speed of 22 m/s, what are the horizontal and vertical

components of the truck’s velocity?

vx = 21 m/s ; vy = 5.7 m/s

TRAJECTORYthe path a

projectile takes

The motion of a projectile is described by:

• Position

• Velocity

• Acceleration

PROJECTILEany launched

object

Types of Projectiles

All 2-D projectiles follow a parabolic

trajectory.

FEED THE MONKEY!!!

Throw at the monkey without gravity.

Throw above the monkey with “gravity on”.

Throw at the monkey at a fast speed with “gravity on”.

Throw at the monkey at a slow speed with “gravity on”.

Independence of x and y motion!

Now we must sign our

“Declaration of Independence”

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

TAKE HOME MESSAGE

Motion in the x-direction is independent of motion in

the y-direction!!!

True or False?

The velocity of a projectile at its highest

point is zero.

Based on your reading, at what angle should

you launch your rockets to get maximum range?

If a ball is tossed up with a velocity of 10 m/s,

what will be its velocity when it returns back to

your hand?

At what point in a trajectory will a projectile have a

maximum height?

A plane flies horizontally at 50.0 m/s. If the plane is 54.0 m

above the ground, how far will the package travel

horizontally before it hits the ground?

166 m

A cat chases a mouse across a 1.0 m high table. The mouse steps out of the way, and the

cat slides off the table at a speed of 5.0 m/s. Where does

the cat strike the floor?

2.3 m from the table

A pelican flying along a horizontal path drops a fish from a height of 5.4 m while

traveling 5.0 m/s. How far does the fish travel horizontally

before it hits the water below?

5.0 m