Projectile Motion is the motion Of objects moving In two

Dimensions under the influenceOf gravity.

Projectiles follow parabolic pathsThis path is called the trajectory.

Projectile motion is free fallWith an initial horizontal velocity.

If a ball is dropped, and another Ball is launched horizontally,

Neglecting air resistance, They will hit the ground at the

Same time!!

By deriving new formulas, We get the following…

Vertical motion of a projectile

Δy = - ½g(Δt)2

Vyf = -gΔt

Vyf2 = -2gΔy

Horizontal motion of a projectileHorizontal motion of a projectile

Δx = vxΔt

vx = vxi = constant

R = v02 sinθg

But what if an object is launchedAt an angle…

Δx = vi (cos θ)Δt

vx = vi (cos θ) = constant

Δy = vi (sin θ)Δt – ½g(Δt)2

vxf = vi(sin θ) - gΔt

vyf2 = vi

2(sin θ)2 – 2gΔy

Certain angles will travel Distances that are equal to

Other angles.

75° = 15°60° = 30°

45° travels the farthest

A ball is launched with an initialVelocity of 4.5 m/s at an angle

Of 66° above the horizontal. WhatWas the maximum height of

The ball? How long did it take For the ball to hit the ground?

y = 0.86m t = 0.84s

Uniform Circular Motion isMotion at constant speed around

A circle with a fixed radius.

Centripetal Acceleration is theCenter directed acceleration of

An object in uniform circular motion

The centripetal force is the Necessary net force exerted in

The centripetal direction to Cause circular motion.

ac = 4π2rT2

Fc = m4π2rT2

v

v

va

r

r

T = the period,The time neededTo one complete

revolution

A 13g rubber stopper is attachedTo a 0.93 m string. The stopper is

Swung in a horizontal circle, Making one revolution in 1.18s. Find the tension force exertedBy the string on the stopper.

0.34 N

A frame of reference is a Coordinate system for specifying

The precise location of objects In space.

Velocity measurements differ In different frames of reference.

For example, if you bounce a ballIn an elevator, the ball will fall at

g relative to the ground, butIts acceleration will be faster

To the elevator when going up.

A Boat traveling east at a speedOf 4 m/s. Peter rolls a marble

With a velocity of 0.75 m/s north,Straight across the deck. WhatIs the velocity of the marble

Relative to the water?

4.1 m/s at 11° north of east