Projectile Motion

Outline

• What is a projectile?

• Strategy for solving Projectile Motion problems

• Galileo’s Theorem

• Examples

Demo: Bring both projectile launchers

Demo: Bring both projectile launchers

What is a Projectile?

• 2-D motion in “free fall” is called projectile motion

• moves in two dimensions (2-D)

• only force is gravity (free fall)

• we ignore air resistance !

QQ48:what is a projectile?

Question:

A basketball is thrown into the air at an angle of 45 to the horizontal. If we can think of the basketball as a projectile, which of the following statements are true?(A) the x-position is constant(B) the y-position is constant(C) the position vector is constant(D) the x-component of the velocity is constant(E) the y-component of the velocity is constant(F) the velocity is constant(G) the x-component of the acceleration is constant(H) the y-component of the acceleration is constant

Strategy for Solving

• Draw a picture with a set of coordinates (always make the y-axis parallel to g)

• Write down the kinematics equations for each axis, and for each object involved in the problem

• Decide which variables in the kinematics equations have values that you know, which are constants, and which are what you are looking to solve for (write these down in an orderly fashion)

• Remember that the time connects the kinematic equations

We know that:

ax= 0, ay = –g = -9.8 m/s2

Projectile motion

x

y

ay

tgvv

vv

oyy

oxx

-,

,

So the equations of motion become

2,

,

2

1tgtvyy

tvxx

oyo

oxo

Equations of Motion

vo

QQ50:Galileo Worked Ex

Example:

If you throw a ball on level ground at speed vo and angle , what would the x and y components of the velocity be ?

Have student stand next to where ball hits. Change angle to show that 45 deg is the max. Then move it to 55 deg, have student stand there, and go to 35 degrees.

Have student stand next to where ball hits. Change angle to show that 45 deg is the max. Then move it to 55 deg, have student stand there, and go to 35 degrees.

vo

x

y

QQ50:Galileo Worked Ex

Example:

If you throw a ball on level ground at speed vo and angle , at what time will it reach the maximum height ?

Have student stand next to where ball hits. Change angle to show that 45 deg is the max. Then move it to 55 deg, have student stand there, and go to 35 degrees.

Have student stand next to where ball hits. Change angle to show that 45 deg is the max. Then move it to 55 deg, have student stand there, and go to 35 degrees.

vo

x

y

Do for next class:

• Read: Sections 6.4

• Suggested problems* : 6.13, 6.16

* one of these problems will be on the Quiz, but with different numbers