- #1
wirefree
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Question: A bullet is fired horizontally aiming at an object which starts falling at the instant the bullet is fired. Show that the bullet will hit the object.
Problem: The conventional way students are advised to address this question is to consider that all limits are bounded: the horizontal distance between the object and the bullet is not too large, the bullet is shot with sufficient speed. The solution, then, simply requires considering the vertical component of the bullet's initial velocity and calculating the distance covered by it in a given time 't', which would be, in fact, equal to that covered by the object in the same time. This concludes the solution.
But, surely, a more rigorous treatment is required; nothing in the question suggests that the setup is perfectly designed.
Approach: Prove that the time taken by the bullet to cover the vertical distance to the horizontal projection of the point where it meets the object is equal to the time taken by the object to cover that same vertical distance is equal to the time taken by the bullet traveling at its horizontal component of velocity to cover the horizontal distance between the gun and the object.
I'll share by attempt in the next post.
At this point, I would appreciate some thoughts on how everyone sees the situation and chooses to address the question.
wirefree
Problem: The conventional way students are advised to address this question is to consider that all limits are bounded: the horizontal distance between the object and the bullet is not too large, the bullet is shot with sufficient speed. The solution, then, simply requires considering the vertical component of the bullet's initial velocity and calculating the distance covered by it in a given time 't', which would be, in fact, equal to that covered by the object in the same time. This concludes the solution.
But, surely, a more rigorous treatment is required; nothing in the question suggests that the setup is perfectly designed.
Approach: Prove that the time taken by the bullet to cover the vertical distance to the horizontal projection of the point where it meets the object is equal to the time taken by the object to cover that same vertical distance is equal to the time taken by the bullet traveling at its horizontal component of velocity to cover the horizontal distance between the gun and the object.
I'll share by attempt in the next post.
At this point, I would appreciate some thoughts on how everyone sees the situation and chooses to address the question.
wirefree