projectile motion the properties of a projectile: – parabolic motion is involved. – the...

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Projectile Motion The properties of a projectile: – Parabolic motion is involved. – The horizontal component of acceleration of a projectile is zero. – The vertical acceleration of a projectile is constant because of gravity. – The horizontal and vertical motions of a projectile are independent, but they share the same time.

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Page 1: Projectile Motion The properties of a projectile: – Parabolic motion is involved. – The horizontal component of acceleration of a projectile is zero. –

Projectile Motion

The properties of a projectile:– Parabolic motion is involved.– The horizontal component of acceleration of a

projectile is zero.– The vertical acceleration of a projectile is constant

because of gravity.– The horizontal and vertical motions of a projectile

are independent, but they share the same time.

Page 2: Projectile Motion The properties of a projectile: – Parabolic motion is involved. – The horizontal component of acceleration of a projectile is zero. –

Vertical Accelerated Motion

(I) a = v2 – v1

Δt (II) Δd = v1Δt + ½a(Δt)2

(III) Δd = ½ (v1 + v2) Δt

(IV) v2

2 = v12 + 2aΔd

(V) Δd = v2Δt - ½a(Δt)2

Page 3: Projectile Motion The properties of a projectile: – Parabolic motion is involved. – The horizontal component of acceleration of a projectile is zero. –

Horizontal Uniform Motion

vav = Δd / ∆t

Page 4: Projectile Motion The properties of a projectile: – Parabolic motion is involved. – The horizontal component of acceleration of a projectile is zero. –

ex. #1:

A marble rolls off a table with a horizontal velocity of 1.93 m/s and onto the floor. The tabletop is 76.4 cm above the floor. Air resistance is negligible.

a) Determine how long the marble is in the air.b) Calculate the range of the marble.c) Calculate the velocity of the marble when it

hits the floor.

Page 5: Projectile Motion The properties of a projectile: – Parabolic motion is involved. – The horizontal component of acceleration of a projectile is zero. –

ex #2:

A projectile launcher is set at an angle of 45° above the horizontal and fires an object with a speed of 2.2 x 102 m/s. The object lands at the same height from which it was launched. Air resistance is negligible. Calculate the object’s:

a) Time of flightb) Horizontal rangec) Maximum heightd) Velocity on impact with the ground

Page 6: Projectile Motion The properties of a projectile: – Parabolic motion is involved. – The horizontal component of acceleration of a projectile is zero. –

ex #3:

Prove using the equations:

Δdy = v1yΔt + ½ay(Δt)2 and Δdx = v1xΔt

That the maximum range of a projectile is given by:Δdx = (v1)2sin2θ

g

Hint: 2sinθcosθ = sin2θ

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