Projectile Motion

Projectile Fired at an Angle - Problems II

Word Problems: Velocity Components, Maximum Height, and Time of Flight

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Do Now warm-up prompt

Angle-Launch Problems II — apply Viy = Visinθ and the kinematics equations to worked word problems: components, max height, and time of flight.

Goalie catching a soccer ball
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Rank the Vertical Velocity from Largest to smallest

Basketball shot arc with points A through F labeled from release to the hoop
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Rank the horizontal displacement from least to greatest. Explain.

Diagram comparing horizontal displacement for several projectiles

Two Velocities, One Football

The football has 2 velocities. Which velocity is the football player matching?

[ Flash ]

Show Me The Physics

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Horizontal velocity.

The football and the football player have a constant horizontal velocity.

Show Me The Physics
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Ex 1

A projectile leaves ground at an angle of 60.° and a speed of 100. m/s.

(a) Find the initial vertical component of the object's velocity

Given

θ = 60.°
Vi = 100. m/s
Viy = ?

Reference diagram
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Viy = Vi(sinθ) = (100. m/s)sin60.°

Viy = 86.6 m/s up

(b) Find the object's maximum height

Given

Viy = 86.6 m/s
ay = -9.81 m/s² (ascending)
dy(max) = ?
Vfy = 0 (at max height)

↓

Vf² = Viy² + 2ad

0² = (86.6 m/s)² + 2(-9.8 m/s²)d

0 = 7499 + -19.6dy  (subtract 7499 from both sides)

-7499 = -19.6(dy)

dy = 382 m

Ex 2

Rock thrown from a cliff at 45 degrees below the horizontal

A rock is thrown from a cliff with initial speed of 40. m/s at an angle of 45.° below the horizontal.

(a) What is the vertical component of the initial velocity?

Given

θ = 45.°
Vi = 40. m/s
Viy = ?

Reference diagram
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Viy = Vsinθ = (40. m/s)sin45.°

Viy = 28 m/s down

(b) If the rock strikes ground in 1.0 sec, what is the height of the cliff?

Given

dy = ? (height)
ay = +9.8 m/s²
t = 1.0 sec
Viy = 28 m/s (from before)

↓

dy = Viyt + (½)at²

= 28. m/s(1.0 sec) + ½(9.81 m/s²)(1.0 sec)²

= 28 m + 4.9 m = 32.9 m down

dy = 33 m down  (2 sig. figs.)

Ex 3

Ball launched from a launcher at 45 degrees, vix = viy = 9.0 m/s, elapsed time to peak = 0.92 s

A ball is fired from a launcher at 45.°, with Vix = Viy = 9.0 m/s. Elapsed time from launch to the peak of the path is 0.92 sec.

At Peak: Vx = ?

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Vx = 9.0 m/s

Total Time in Air?

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1.84 sec (twice the time to peak)

actually 1.8 sec  (2 sig. figs.)

What will the horizontal velocity of the baseball be just before it hits the ground?

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9 m/s — Vx is constant

Multiple Choice: Maximum Range

Given A projectile lands at the same height from which it was launched. Which initial velocity will result in the greatest horizontal displacement of the projectile? Neglect friction. (1) Vi=10. m/s at 45 degrees (2) Vi=10. m/s at 30 degrees (3) Vi=20. m/s at 45 degrees (4) Vi=20. m/s at 60 degrees
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Choice 3

The Monkey and the Hunter

[ Monkey and Hunter ]   [ HTML5 ] — Don Ion

(offsite)

Flash Physics - Don Ion

St. Mary's U. Astronomy and Physics Dept.

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Diagram of the Monkey and Hunter demonstration apparatus
Projectile Motion: The Monkey and Hunter Demonstration. A cannon fires a golf ball at a stuffed toy monkey held by an electromagnet; the magnet releases the monkey the instant the ball leaves the cannon.
Monkey and hunter apparatus
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Projectile Motion Game — Show Me The Physics

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