Question**: A projectile is launched at an angle of 45 degrees with an initial speed of 20 m/s. What is the maximum height reached by the projectile? (Use \( g = 9.8 \, \textm/s^2 \)) - Tacotoon
Question: A projectile is launched at an angle of 45ð with an initial speed of 20 m/s. What is the maximum height reached by the projectile? (Use ( g = 9.8 , \ ext{m/s}^2 ))
Question: A projectile is launched at an angle of 45ð with an initial speed of 20 m/s. What is the maximum height reached by the projectile? (Use ( g = 9.8 , \ ext{m/s}^2 ))
Understanding Projectile Motion and Maximum Height
Understanding the Context
When a projectile is launched at an angle, its motion can be broken down into horizontal and vertical components. The maximum height is determined solely by the vertical motion, specifically the component of velocity perpendicular to the ground.
Given:
- Launch angle ( \ heta = 45^\circ )
- Initial speed ( v_0 = 20 , \ ext{m/s} )
- Acceleration due to gravity ( g = 9.8 , \ ext{m/s}^2 )
Step 1: Vertical Component of Initial Velocity
Image Gallery
Key Insights
Only the vertical component contributes to reaching maximum height. It is calculated using:
[
v_{y} = v_0 \sin \ heta
]
Substituting ( \ heta = 45^\circ ) and ( \sin 45^\circ = rac{\sqrt{2}}{2} ):
[
v_y = 20 \ imes rac{\sqrt{2}}{2} = 10\sqrt{2} pprox 14.14 , \ ext{m/s}
]
🔗 Related Articles You Might Like:
📰 What You Didn’t Know About MusicalCalifornia Will Shock You 📰 The Hidden Stories Behind MusicalCalifornia’s Greatest Hits 📰 MusicalCalifornia’s Secret Behind the Sound That Defined a Generation 📰 Insane Hercules Disney Movie Facts You Thought Happened Only In Myth Heres The Shocking Truth 📰 Inside Griffith The Hidden Truth Behind Its Ghostly Allure You Wont Believe 7 📰 Inside Grizzly Jack Bear Resort Where Grizzlies Rule And Luxury Calls 📰 Inside Grodds Dc Universe The Dark Secret Behind His Rise To Power 📰 Inside Gta 6 News What Rumors Finally Turned Fact And What That Means For Gamers 📰 Inside Guilty Gear The Brutal Truth Behind The Battle That Defined A Generation 📰 Inside Gumball Wattersons Dark Secret You Wont Wake Up After This Twistrevealed 📰 Inside Gundam Requiem For Vengeance The Epic Sagas Most Powerful Payoff You Didnt See Coming 📰 Inside Guy Gardners Game Changing Strategy That Few Know About 📰 Inside Gwenpool The Secret Thats Sparking Endless Buzz Online 📰 Inside Haganezuka The Astonishing Reason Thousands Are Obsessedyou Must See 📰 Inside Hannah Marie Royals Journey The Secrets Behind Her Rising Star Power 📰 Inside Hannibal Nbcs Nbc Verdict The Moment That Made Him A National Sensation 📰 Inside Haosetv The Game Changer Youve Been Searching For In Tv Streaming 📰 Inside Harvest Hall The Night That Unlocked A Legendary MysteryFinal Thoughts
Step 2: Use Kinematic Equation to Find Maximum Height
At maximum height, the vertical velocity becomes zero (( v_y = 0 )). Using the velocity equation:
[
v_y^2 = u_y^2 - 2gh_{\ ext{max}}
]
Where:
- ( v_y = 0 ) (at peak)
- ( u_y = 10\sqrt{2} , \ ext{m/s} )
- ( h_{\ ext{max}} ) is the maximum height
Rearranging:
[
0 = (10\sqrt{2})^2 - 2 \cdot 9.8 \cdot h_{\ ext{max}}
]
[
0 = 200 - 19.6 \cdot h_{\ ext{max}}
]
Solving for ( h_{\ ext{max}} ):
[
h_{\ ext{max}} = rac{200}{19.6} pprox 10.2 , \ ext{meters}
]
