Projectile angle and maximum height

In summary, the conversation is about finding the projection angle at which a projectile's range is equal to its maximum height. The conversation mentions using double angle identities to solve the question, but the person asking for help is unsure if they are necessary. They also discuss the equation for maximum height and range, and someone suggests solving for the maximum height and setting it equal to the range.
  • #1
ThomasMagnus
138
0
At what projection angle will the range of a projectile equal its maximum height?


I am having a lot of trouble with this one. Is there any way to solve this question without using double angle identities?

I know that this should be the first step:

Max height when Vy=o
Vfy2=Voy2 + 2(a)(dy)

0=(Vo2 + 2(a)(d)

Range= Vo2 sin2(theta)/g


I'm stuck here. Can anyone help me?

Thanks!
 
Physics news on Phys.org
  • #2
What's wrong with double angle identities? They can always be undone. What does sin(2θ) become?

You're on the right track. Solve for the maximum height of the trajectory and set it equal to the range. Be sure to keep track of what's the total velocity and what are components.
 

1. What is the equation for calculating the maximum height of a projectile?

The equation for calculating the maximum height of a projectile is h = (v2sin2θ)/2g, where h is the maximum height, v is the initial velocity of the projectile, θ is the launch angle, and g is the acceleration due to gravity.

2. How does the launch angle affect the maximum height of a projectile?

The launch angle has a significant impact on the maximum height of a projectile. The maximum height will be achieved when the launch angle is 90°, as the vertical component of the initial velocity will be the highest. If the launch angle is lower, the maximum height will also be lower.

3. Can the maximum height of a projectile be greater than the initial height?

Yes, the maximum height of a projectile can be greater than the initial height. This can occur when the launch angle is between 0° and 90°. If the initial height is greater than the maximum height, the projectile will not reach its maximum height and will fall back to the ground before then.

4. How does air resistance affect the maximum height of a projectile?

Air resistance can decrease the maximum height of a projectile. This is because air resistance acts in the opposite direction of the projectile's motion, slowing it down. Therefore, the projectile will not have enough velocity to reach its maximum height, and it will be lower than if there was no air resistance.

5. What are some real-life applications of understanding projectile angle and maximum height?

Understanding projectile angle and maximum height is crucial for a variety of real-life applications. For example, it is essential in sports such as basketball and golf, where players need to understand the optimal angle to launch the ball to achieve the maximum height and distance. It is also crucial in fields such as engineering and physics, where calculating projectile motion is necessary for designing structures and predicting the trajectory of objects.

Similar threads

Find Projectile Flight Time Given Only Maximum Height
    • Introductory Physics Homework Help
Replies
4
Views
1K
A ball is thrown w/initial speed vi at an angle 𝜃i with the horizontal
    • Introductory Physics Homework Help
Replies
5
Views
289
I need opinions on a Projectile Motion problem that I made up
    • Introductory Physics Homework Help
Replies
11
Views
791
Projectile Motion Question: A projectile is fired on a long flat firing range....
    • Introductory Physics Homework Help
Replies
3
Views
3K
Projectile motion with (constant) wind velocity
    • Introductory Physics Homework Help
Replies
8
Views
1K
Projectile Motion on the Moon: Finding the Optimal Launch Angle Using Equations
    • Introductory Physics Homework Help
Replies
2
Views
2K
Hitting a rocket with a projectile
    • Introductory Physics Homework Help
2
Replies
53
Views
3K
Deriving an equation to find theta: Projectile motion
    • Introductory Physics Homework Help
Replies
7
Views
2K
Relationship between Launch height and range of a projectile
    • Introductory Physics Homework Help
Replies
15
Views
21K
Projectile motion -- how long does it take the projectile to reach maximum height?
    • Introductory Physics Homework Help
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top