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Stones are thrown horizontally with the same velocity from the tops of two different buildings. One stone lands twice as far from the base of the building from which it was thrown as does the other stone.Find the ratio of the height of the taller building to the height of the shorter building.

$\frac{H_{1}}{H_{2}}=4$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

Lectures

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In mathematics, algebra is…

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A rock is dropped at the s…

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You're atop a buildin…

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Matching heights $A$ stone…

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A rock $(m=2 \mathrm{kg})$…

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So the question states that two rocks are thrown off to different size buildings. Let's just say this building is height H two, and the other building is height, each one, and they're both thrown with a speed V in the horizontal direction. Uh, and we're also told that the rock thrown from the higher building goes twice the horizontal distance that the rock from the lower building goes. And we're trying to find what the ratio of the, uh building heights eyes. And so the first thing we should look at is the relationship between the times that each rock travels in the air. So we know from the equation the velocity times. The time is equal to change in displacement in the horizontal direction, that if we increase our displacement by a factor of two and we keep the velocity of the rock the same, this time must also increase by a factor of two. Knowing this, this means that the rock thrown from the higher building must travel twice the time the rock from the lower building travels. Now that we know this, we can just use our Kinnah Matic equations to figure out what this ratio between the heights of the buildings are. So let's say H to the height of the tall building is going to be equal to, um its initial the initial vertical velocity of the rock plus 1/2 a T squared. And we know that the initial vertical velocity of the rock is zero because it's learned horizontally. So this will cancel. And we know that the time here is twice the time of the small of the small building rock. So we can say that this travel time here his tea So this once again must be twice t so we can substitute to t into here and we get that H two is equal to 1/2 times a times for T Square. We can do the same thing for H one. Once again, this is going to be zero. So you get 1/2 times a times T squared. This is just tea because we're naming this time here, t this time here. And so when we take the ratio of, uh, H two over h one, we find that the ratio is just four because all the all of these terms canceled. The one half's canceled A is canceled. The T Square's cancel. We're just left with four and that's our in

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