projectile motion ► all objects move in air along a similar path. explain the shape of that path....

Projectile MotionProjectile Motion

►All objects move in air along a similar All objects move in air along a similar path. Explain the shape of that path.path. Explain the shape of that path.

►What is this curve called? (math class)What is this curve called? (math class)


►PARABOLAPARABOLA

►Can be represented mathematicallyCan be represented mathematically

►Same old stuffSame old stuff


Combining the Combining the Laws of MotionLaws of Motion and what and what we know about we know about vectorsvectors, we can predict , we can predict the path of projectiles.the path of projectiles.

REMEMBER… X & Y COMPONENTS ARE REMEMBER… X & Y COMPONENTS ARE INDEPENDENT OF EACH OTHER!!!!!INDEPENDENT OF EACH OTHER!!!!!


►ProjectileProjectile – An object with independent – An object with independent vertical (y) and horizontal (x) motions vertical (y) and horizontal (x) motions that moves through the air only under that moves through the air only under the influence of gravity after an initial the influence of gravity after an initial thrustthrust

►TrajectoryTrajectory – the path of a projectile – the path of a projectile through the airthrough the air

Projectile ProblemProjectile Problem

You accidentally throw your car keys You accidentally throw your car keys horizontally at 9.0 m/s from a cliff 74 horizontally at 9.0 m/s from a cliff 74 m high. How far away from the base m high. How far away from the base of the cliff should you look for your of the cliff should you look for your keys?keys? X Y

Projectile ProblemsProjectile Problems

►Organize information in terms of X and Organize information in terms of X and Y componentsY components

X Y


►Organize information in terms of X and Organize information in terms of X and Y componentsY components

X Y

Δdy = 74m Vx = 9.0 m/s

dx = ?


►What information, that is not stated in What information, that is not stated in the problem, do we know.the problem, do we know.

X Y

Δdy = 74m

ay = 9.8 m/s2

vyi = 0 m/s at peak of parabola for 2nd half of the trip

Vx = 9.0 m/s

dx = ?


►What one variable is part of both the x What one variable is part of both the x and y components?and y components?

TIMETIME►To solve for dTo solve for dxx, we need the time, we need the time

vvxx = d = dxx / / tt


►Can’t solve for Can’t solve for t t using the X using the X components?components?

►Can we solve for Can we solve for tt using the Y? using the Y?

YEP!YEP!


Y’sY’sΔdy = 74m

ay = 9.8 m/s2

vyi = 0 m/s at peak of parabola

t = ?

Use 2nd half of parabolic motion, where vyi = 0 m/s (peak of parabola)

Δdy = vyit + ½ ayt2


►Solve for tSolve for tdy = vit + ½ at2

74m = 0 + ½ (9.8m/s2) t2

Therefore,

t = √(74m / (½ (9.8m/s2) )

t = 3.9s


►Knowing the time (3.9s) and vKnowing the time (3.9s) and vxx (9.0m/s), (9.0m/s), we can solve for dwe can solve for dxx (where we should (where we should look for our keys)look for our keys)

►Using VUsing Vxx = d = dxx / t / t

9.0m/s = d9.0m/s = dxx / 3.9s / 3.9s

ddxx = 35 m = 35 m

We should look 35 m from the cliffWe should look 35 m from the cliff

Projectile Motion Practice Projectile Motion Practice ProblemProblem

►A stone is thrown horizontally at a A stone is thrown horizontally at a speed of +5.0 m/s from the top of a speed of +5.0 m/s from the top of a cliff 78.4 m high. cliff 78.4 m high. How long does it take the stone to reach How long does it take the stone to reach

the bottom of the cliff?the bottom of the cliff? How far from the base of the cliff does the How far from the base of the cliff does the

stone strike the ground?stone strike the ground? What are the horizontal and vertical What are the horizontal and vertical

components of the velocity of the stone components of the velocity of the stone just before it hits the ground?just before it hits the ground?

projectile motion ► all objects move in air along a similar path. explain the shape of that path....

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