Projectile Motion

Projectile Fired at an Angle - Problems II

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

← Angle Problems All Lessons Circular Motion →
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
Do Now

Rank the Vertical Velocity from Largest to smallest

Basketball shot arc with points A through F labeled from release to the hoop
Do Now

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

↓

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
↓

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
↓

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.

| Onsite |

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
Projectile Motion Game
Projectile Motion Game — Show Me The Physics

Play It Yourself

Projectile Motion Game — Show Me The Physics

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. A football player runs under a pass and catches it. Which of the ball's velocities is the player matching?

2. A projectile is launched at 40. m/s at 30.° above horizontal. What is its initial vertical velocity?

3. A projectile has Viy = 19.6 m/s up. What maximum height does it reach? (g = 9.8 m/s²)

4. A ball is launched at 45° with Vix = Viy = 9.0 m/s. What is its horizontal velocity just before it hits the ground?

5. A projectile lands at its launch height. Which launch gives the greatest horizontal displacement?

NYSSLS Regents Practice · Projectile Motion · Models & Predictions

The Monkey and the Hunter

In a classic demonstration, a dart launcher is aimed directly at a toy monkey hanging from an electromagnet. When the dart is launched, a switch turns off the magnet, so the monkey starts to fall at the same instant. Air resistance is negligible, and the dart reaches the monkey’s horizontal position before either hits the floor.

What happens?

▶ Want a challenge? Open 6 more Regents-style questions  (harder · mixed formats)

Challenge score: 0 / 6

Support or Refute · Justify

C1. A student makes the following claim.

Claim: If the dart were launched at a greater speed (still aimed directly at the monkey), it would pass above the monkey.

Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.

Multiple choice

C2. A football is kicked at 25 m/s at 53° above level ground (vx = 15 m/s, vy = 20. m/s). How long is it in the air?

Substitute values

C3. In one trial, the dart reaches the monkey’s horizontal position 0.40 s after launch. Substitute numerical values into a mathematical representation that can be used to determine how far the monkey falls before it is hit. Then calculate the distance.

d = ½( m/s2)( s)2 = m
Select all that apply

C4. Place a check mark in three boxes to indicate the conditions required for the dart to hit the monkey in this demonstration.

Multiple choice

C5. In a real game, air resistance acts on the ball. How does this affect the path compared with the ideal model?

Constructed response

C6. Suppose the electromagnet’s switch is faulty and the monkey is released 0.10 s after the dart is launched. Predict whether the dart passes above or below the monkey, and explain your reasoning.

Circular Motion →