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 \( g = 9.8 \, \textm/s^2 \)) - Malaeb
Question: A projectile is launched at an angle of 45ÃÂð 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 45ÃÂð 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:
📰 sparkling water recipes 📰 cullinan park 📰 finance of america reverse llc 📰 Denim Levi Vest 9731335 📰 Jersey Freeze 3118134 📰 Scooby Doo And The Cyber Chase The Scariest Tech Mystery Ever 5970462 📰 Hidden Cuteness The Ultimate Cute Femboy Look Everyone Needs You Wont Believe The Details 8793781 📰 Yahoo Tsla Stock Is Soaringinvestors Are Racing To Buy Before It Blows Up 6417345 📰 Tz 62208 Sqrt622082494 2494 Earth Years 7366100 📰 You Wont Believe What This Pink Carhartt Jacket Hides Beneath Its Stunning Fabric 2050224 📰 Json Comment 5643309 📰 G5 Sqrt53 Sqrt8 2Sqrt2 1965825 📰 Define Homogeneous Mixture 9612614 📰 5 Ii R34 Overwatch Explosion Are You Getting Caught Game Changer Inside 5502224 📰 Esyt 6111957 📰 Watch The Game Changing Hd Close Method That No Creator Should Miss 4154486 📰 Al Nassr Exposed As Neoms Hidden Enemy In Next Generation Solar Era Showdown 374791 📰 South Park Season 27 Episode 1 Full Episode 6534285Final 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}
]
