Why is it so hard to Why is it so hard to get rubbish in the get rubbish in the

bin?bin?

Projectile motionProjectile motion

Remember Newton’s Remember Newton’s 11stst law of motion law of motion

– If there is no force acting on an object If there is no force acting on an object there is no acceleration, so the object there is no acceleration, so the object will be stationary or will move at a will be stationary or will move at a constant velocity.constant velocity.

Definition of a projectileDefinition of a projectile

Any object moving Any object moving through air without through air without its own source of its own source of power and only power and only under the influence under the influence of gravity…of gravity…

eg: a golf ball after eg: a golf ball after being hit.being hit.

Compare a ball rolling off a Compare a ball rolling off a desk to one being droppeddesk to one being dropped

The balls land at the The balls land at the same time because same time because the force of gravity is the force of gravity is the same on both.the same on both.

The rolled ball The rolled ball continues moving continues moving forward at the same forward at the same speed as on the desk: speed as on the desk: there is no horizontal there is no horizontal force to slow it down.force to slow it down.

Key physics ideas for Key physics ideas for projectilesprojectiles

Divide the story into horizontal and Divide the story into horizontal and vertical directions.vertical directions.

There are no horizontal forces acting so There are no horizontal forces acting so the velocity is constant and we use the the velocity is constant and we use the equation v = d/t.equation v = d/t.

The only vertical force is gravity so we The only vertical force is gravity so we know the acceleration is 9.8msknow the acceleration is 9.8ms-2-2. .

Time of flight is the only thing common to Time of flight is the only thing common to the vertical and horizontal movements.the vertical and horizontal movements.

Use the five equations of motion.Use the five equations of motion.

Solving Projectile problems: the Solving Projectile problems: the first type…first type…

Facts about simple Facts about simple vertical projectilesvertical projectiles

Throwing something Throwing something straight up or downstraight up or down

Acceleration is Acceleration is --

9.8ms9.8ms-2-2 on the way up on the way up and and ++9.8ms9.8ms-2-2 on the on the way downway down

Velocity is 0msVelocity is 0ms-1-1 at the at the top of the motiontop of the motion

Q: A tennis player throws up a ball at 5.8msQ: A tennis player throws up a ball at 5.8ms--

11 for a serve. What is the maximum height for a serve. What is the maximum height the ball reaches?the ball reaches?

Fill in the information Fill in the information you knowyou know

Vi = Vi = Vf = Vf = a = a = d = d =

Choose an equation of Choose an equation of motionmotion

Substitute and solveSubstitute and solve

Use the problem Use the problem and common senseand common sense

Vi = 5.8 msVi = 5.8 ms-1-1

Vf = 0 msVf = 0 ms-1-1

a = -10 msa = -10 ms-2-2 d = ?d = ? VfVf22 = Vi = Vi22 +2ad +2ad

0 = 5.82 + 2(-10)d0 = 5.82 + 2(-10)dd = 1.7m d = 1.7m

Q: A tennis ball is thrown up at 3.9msQ: A tennis ball is thrown up at 3.9ms -1-1. How . How long does it take to reach its maximum height?long does it take to reach its maximum height?

Q: A rock is dropped off a cliff 75m high. How Q: A rock is dropped off a cliff 75m high. How long does it take to reach the bottom of the long does it take to reach the bottom of the

cliff? What is its speed after 2s?cliff? What is its speed after 2s?

Vi = 3.9 msVi = 3.9 ms-1-1, Vf = , Vf = 0ms0ms-1-1, , a = -10 ms-2, t = ?a = -10 ms-2, t = ?

Vf = Vi + atVf = Vi + at 0 = 3.9 +-10t0 = 3.9 +-10t t = 0.398st = 0.398s

d = 75 m, Vi = 0 msd = 75 m, Vi = 0 ms-1-1, a = -, a = -10 ms10 ms-2-2

d = Vit + 1/2atd = Vit + 1/2at22

75 = 1/2 (-10)t75 = 1/2 (-10)t22

t = 3.9st = 3.9s

Vf = Vi + at = 0 +10x2Vf = Vi + at = 0 +10x2== 20ms20ms-1-1

Solving projectile problems: the second Solving projectile problems: the second typetype

Half projectiles Half projectiles At position A the At position A the

velocity is only velocity is only horizontalhorizontal

At position B the At position B the horizontal velocity is horizontal velocity is the same but there is the same but there is a vertical componenta vertical component

A

B

Range

Q: A person fires a gun horizontally from the Q: A person fires a gun horizontally from the top of a cliff 70m high. The bullet travels out top of a cliff 70m high. The bullet travels out

at 100msat 100ms-1. -1. Two possible Q…Two possible Q…What is the time to the What is the time to the

bottom?bottom?

Since time is the dame Since time is the dame vertically or vertically or horizontally, use either horizontally, use either vertical or horizontal, vertical or horizontal, eg: vertically,eg: vertically,

Vi = 0 msVi = 0 ms-1-1, a = 10 ms, a = 10 ms--

22, d = 70 m, d = 70 m d = Vit + 1/2atd = Vit + 1/2at22

70 = 0 + ½(10) t70 = 0 + ½(10) t22 t = 3.7st = 3.7s

What is the range? What is the range? Must use the Must use the horizontal horizontal information,information,

Vi = 100 msVi = 100 ms-1-1, a = 0 , a = 0 msms-2-2, t = 3.7 s, t = 3.7 s

d = vt = 100(3.7) d = vt = 100(3.7)

= 370m= 370m

Q: A duck shooter fires a bullet horizontally at Q: A duck shooter fires a bullet horizontally at 80ms80ms-1-1 to hit a duck. They miss, and the bullet to hit a duck. They miss, and the bullet

comes down 1.8m to hit the ground. Find the time comes down 1.8m to hit the ground. Find the time for the bullet to hit the ground and the distance for the bullet to hit the ground and the distance

away from the shooter that it lands.away from the shooter that it lands.

Q: Q: A food crate is dropped from a plane A food crate is dropped from a plane flying horizontally at 160ms flying horizontally at 160ms -1-1. If the crate . If the crate takes 12s to hit the ground, from how high takes 12s to hit the ground, from how high was it dropped. How far does the crate was it dropped. How far does the crate travel horizontally from the point where it travel horizontally from the point where it was dropped?was dropped?