What Are the Minimum and Maximum Launch Speeds to Get a Match into a Basket?

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To determine the minimum and maximum launch speeds for a match to enter a waste paper basket, the match must be thrown at a 45-degree angle from a distance L, where L is the horizontal distance to the basket. The match reaches its maximum height at 2D, the height of the basket, and must land within the basket's diameter D. The calculations involve using projectile motion equations, focusing on the initial velocity v and the gravitational constant g. Ignoring air resistance, the launch speeds can be expressed in terms of D and g. The problem emphasizes the importance of understanding the relationship between launch angle, distance, and height in projectile motion.
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there is a waste paper basket of diameter D and height 2D. u throw a burning match from the same level as the bottom of the basket ,the horizontal distance between the near side of basket and the point from which u throw the match. u launch the match at 45 degrees with the horizontal. find the minimum and maximum values of the launch speed so that the match enters the basket.(ingore air resistance and give ans in terms of D and g).



please help 'sob'
 
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Hi riddhish! :smile:

First, weed out the irrelevant detail …

The question is the same as:
Launch an object at 45º so that, after it reaches its greatest height, it reaches height 2D between L and L + D, where L is the initial horizontal distance.

So start "Let the initial velocity be v", and carry on from there! :smile:
 
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