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Projectile Motion

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Projectile Motion

- Projectile Motion (7 min)
- The path of motion an object when it is thrown or launched into the air
- The shape of the path is a parabola
- Also called a trajectory

- An object has the vertical and horizontal motion simultaneously
- The vertical motion is a free fall due to gravity, acceleration downward (g = –10 m/s2)
- Mass of a falling object doesn’t change the vertical speed and acceleration

- The horizontal motion is a constant velocity – no horizontal acceleration

- The vertical motion is a free fall due to gravity, acceleration downward (g = –10 m/s2)
- The vertical motion and horizontal motion are INDEPENDENT of each other
(Ex) An object is thrown horizontally from the top of a building. What will be its trajectory?

- Horizontal motion has a constant velocity
- Assume the air resistance is negligible
- ax = 0 m/s2

trajectory, a parabola

Divide the projectile (≈object) motion into vertical and horizontal motions

- vertical motion
- straight up or down regardless of the surface
- A gravitational force acts on the object

- Time for horizontal motion = Time for vertical motion
- Common mistake: △ttotal = △tx + △ty
- The correct thinking: △ttotal = △tx = △ty
- An object thrown out of a horizontally moving airplane has the same velocity as the plane.

vi,x = vf,x

vi,y = 0 if the object is just dropped vf,y =

△tx=△ty= △ttotal

△x =

△y =

ax = 0

ay = g = -9.8 m/s2

- A bullet is shot horizontally and another one is dropped at the same time

- Draw a diagram and identify all info
- Keep x-component variables and y-component variables separate
- time is the only variable that is the same for both components

- Know what you are solving for
- Select the proper formulas
- The formulas are used for both components
- Be careful not to mix x- and y- components when plugging values into the formula
- Choose the right sign for the variable

- Check to see if the answer is reasonable – sign, value, etc

- A movie director is shooting a scene that involves dropping a stunt dummy out of an airplane and into a swimming pool. the plane is 10.0 m above the ground, traveling at a velocity of 22.5 m/s in the positive x direction. The director wants to know where in the plane’s path the dummy should be dropped so that it will land in the pool. (You will need this problem to solve #3 of Practice 3D, Pg 102)

2)A stone is thrown horizontally at a speed of 5.0 m/s from the top of a cliff that is 78.4 m high.

a) How long does it take the stone to reach the bottom of the cliff?

b) How far from the base of the cliff does the stone hit the ground?

c) What are the horizontal and vertical components of the stone’s velocity just before it hits the ground?

3) Lucy and her friend are working at an assembly plant making wooden toy giraffes. At the end of the line, the giraffes go horizontally off the edge of the conveyor belt and fall into a box below. If the box is 0.6 m below the level of the conveyor belt and 0.4 m away from it, what must be the horizontal velocity of giraffes as they leave the conveyor belt?

4) You are visiting a friend from elementary school who now lives in a small town. One local amusement is the ice-cream parlor, where Stan, the short-order cook, slides his completed ice-cream sundaes down the counter at a constant speed of 2.0 m/s to the servers. If the servers catch the sundaes 7.0 cm from the edge of the counter, how far do they fall from the edge of the counter to the point at which the servers catch them? (No friction on the counter)

A projectile launched at a angle

1) forms a complete parabola

2) ½ left of the parabola is symmetrical to ½ right – velocity, time, displacement

3) constant horizontal velocity

*The horizontal acceleration = 0

- vertical velocity: the same magnitude with the opposite sign (going up “+” velocity; coming down “–” velocity )
*The vertical acceleration = –9.8 m/s2 regardless going up or coming down

5) The max (vertical) height

- occurs at ½ of flight time (∆t)
- has vy = 0 and vx = vi,x
6) Range (R) = the horizontal distance (a scalar quantity) a projectile travels

1) A ball is launched at 4.5 m/s at 66˚ above the horizontal. What are the max height and flight time of the ball?

vi = 4.5 m/s

ө = 66˚

2. A player kicks a football from ground level with an initial velocity of 27.0 m/s, 30.0° above the horizontal, as shown in Figure 6-4. Find each of the following. Assume that air resistance is negligible.

the ball’s hang time

b. the ball’s maximum height

c. the ball’s range

3) The player in problem 2 then kicks the ball with the same speed, but at 60.0°from the horizontal. What is the ball’s hang time, range, and maximum height?