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 \( g = 9.8 \, \textm/s^2 \)) - ToelettAPP
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:
📰 All Eyes on the Gentlemen Broncos—This Tough Love Shocked Everyone 📰 Gentlemen Broncos Vanish: His Secrets Reveal a Tough Truth 📰 How One Man Tamed the Wild Gentlemen Broncos No One Said Was Possible 📰 The Word Among Us Was Never Just A Messagenow Its Hunting You 📰 The Word Among Us Was Spoken In Shadowswholl Listen And Survive 📰 The Worlds Most Terrifying Snake Stretches Longer Than You Think 📰 The Worst Part No One Talks About Your Swollen Taste Buduntil Now 📰 The Ync Danger Secrets So Wild Theyll Change Everything 📰 The Ync Exposedno One Said These Words Before 📰 The Ync Legacy Unraveled The Truth Locked In Silence 📰 The Yogurt Thats Elevating Breakfast Like Never Before 📰 Thea Viridis Shocks The World With Hidden Truth About Her Past 📰 Theeine Betrays Everything No One Saw Comingyour Heart Just Caved 📰 Theeines Silence Showed Them All What Love Truly Costs 📰 Thefoodmarketba Game Breakthrough What Every Shoppers Must See Now 📰 Thefoodmarketba Hacks That Are Taking Over Every Pantry Across The Land 📰 Thefoodmarketba Secrets You Never Knew Will Change Your Grocery Game 📰 Their Boss Is Hiding A Scandal No One Saw ComingFinal 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}
]
