If I decided to get a dog, and then take this dog for a walk/run. Consider the following idea.

If the dog can run at a constant speed twice as fast as my constant speed. And it has the odd habit of running from me to our destination and back to me continuously.

HOW MUCH FURTHER WILL THE DOG GO?

How can you figure this out?

Write down what you know.

TIME

Twice as far

This concept is true when we think of projectile motion!

We are going to take these 3 equations and make six!!

What do we have in common?

Take the two position equations

Let initial position be zero

Y

If we assume the ball also lands on the

ground

(or any same height that it started)

I can set y = 0 and multiply some a term

Use trig identity and

solve for x

A projectile is fired with an initial speed of 65.2 m/s at an angle of 34.5 degrees above the horizontal on a long flat firing range.

Max height

Total time in air

Range

Velocity at 1.5 s.

h = 69.58 69.6 m

t = 7.5366 7.54 s

range = 404.96 405 m

v(1.5) =40.396 at 33.38

40.4 m/s 33.3 degrees

**Practice by yourself**

A hunter aims directly at a target (on the same level) 75.0 m away.

If the bullet leaves the gun at a speed of 180 m/s by how much will it miss the target?

At what angle should the gun be aimed so as to hit the target?

A hunter aims directly at a target (on the same level) 75.0 m away.

If the bullet leaves the gun at a speed of 180 m/s by how much will it miss the target?

At what angle should the gun be aimed so as to hit the target?

**.85 m**

**.65 degrees**

**Practice with a friend**

A shot putter throws the shot with an initial speed of 15.5 m/s at a 34.0 degree angle to the horizontal. Calculate the horizontal distance traveld by the shot if it leaves th eathlete's hand at a height of 2.20 m above the ground.

A shot putter throws the shot with an initial speed of 15.5 m/s at a 34.0 degree angle to the horizontal. Calculate the horizontal distance traveld by the shot if it leaves th eathlete's hand at a height of 2.20 m above the ground.

**25.7 m**

Acceleration

It seems like we have already solved for this,

realize the previous usages of acceleration were

with a constant acceleration, this is not always the case.

By definition average acceration is the

change of velocity in time:

note they are vectors, if you know the direction

of one, you know the other.

This acceleration will cause the particle to

A. slow down and curve downward.

B. slow down and curve upward.

C. speed up and curve downward.

D. speed up and curve upward.

E. move to the right and down.

Instantaneous Acceleration

is solved the same way as instantaneous velocity, we let the time go to zero, and our limit becomes a derivative

Kinematics in 2 dimesions

What can I say.

It is just kinematics, with x's and then

kinematics with y's.

If you are feeling equation deprived, some

will come as we do projectile motion.

"Why does the trajectory at every point matter? " " Can we go over trajectory lines a little bit more?"

"Could you go over instantaneous acceleration? Also how is projectile motion two independent motions?"

"Why does the acceleration of the ball point upward at the bottom of the hill? I'm just having a hard time picturing that."

" Can we talk about the acceleration components of a projectile?"

" Can you go how to find the tangent line from the trajectory?"

"Can you go over the differences between constant acceleration and instantaneous acceleration in a trajectory graph?"

"could you go over 2-dimensional acceleration? Its not 100% clear to me yet."