Angle at which distance is longest?

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In summary, the conversation discusses the concept of projectile motion and how the maximum distance of a ball depends on the initial velocity and angle. The question posed is about finding the angle at which a ball will land on a tower with a different height from its initial position, and whether the formula for finding this angle changes depending on the situation.
  • #1
Irrelativity
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I have a question about projectory motion.

I know that if ball is thrown by a person with a initial velocity v(only x and ycomponents), a maximum distance d (distance of x component) can be achived at angle of 45 degree (an angle between the initial velocity and x component of the velocity). But this is only true when the initial position of y component is the same as the terminal position of y conpoment. Here's the my question: how do you guys find the angle at which when the height of a landing position is not the same as the height of the initial position (i.e. Initial y is not equal to terminal y)? Let's say the ball lands on a tower which has a height h with minimum velocity. What's the formula to find the angle?
 
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  • #2
You mean, what is the angle for the ball to land on the tower? Or to reach maximum range?
Or you have a series of towers and you want to reach the farthest tower possible?
 
  • #3
Does the attachment answer your question?
 

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  • Projectile_Motion.pdf
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1. What is the angle at which distance is longest?

The angle at which distance is longest is known as the optimal angle. It varies depending on the specific scenario, but it is typically around 45 degrees.

2. How do you calculate the optimal angle?

The optimal angle can be calculated using trigonometric functions such as sine, cosine, and tangent. It involves finding the angle that maximizes the distance between two points.

3. What factors affect the optimal angle?

The optimal angle is affected by various factors such as the distance between the two points, the slope of the terrain, and any obstructions in the path.

4. Why is the optimal angle important?

The optimal angle is important in various fields such as engineering, architecture, and physics. It helps determine the most efficient path for objects to travel and can impact the design and construction of structures.

5. Can the optimal angle be applied in real-life situations?

Yes, the optimal angle can be applied in many real-life situations. For example, it can be used to design the most efficient ramp for a wheelchair, determine the best angle for solar panels to receive maximum sunlight, and even in sports such as golf and basketball to achieve the longest distance for a shot.

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