Brock Brown

2022-01-07

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.

Bukvald5z

Beginner2022-01-08Added 33 answers

Step 1

By neglecting the resistance of the air, both stones will experience an acceleration only on the vertical axis which is the acceleration of the gravity, and the velocity in the horizontal axis is constant. Therefore, the following equation describes the motion of the stones in the vertical axis:

since both stones are thrown horizontally, the vertical initial velocity is zero, so:

the first stone will make a vertical displacement magnitude equals the height of the first building

the second stone will make a verticaldisplacement magnitude equals the height of the second building

Step 2

The distance in the horizontal axis is given by:

Both stones are thrown horizontally with the same velocity (say

and for the second stone is,

hence, the height of the two building will become:

but the first stone lands twice as far from the base of the base of the building which means

clearly

Papilys3q

Beginner2022-01-09Added 34 answers

Distance from the base of the building to place where stone landing:

where v is velocity, t is time.

Time can be found from:

where h is height of the building

Therefore:

Answer: 4

karton

Expert2022-01-11Added 613 answers

Answer:

4 times taller

Explanation:

The horizontal distance travelled by a projectile is

where

The total time of the fall can be found by analyzing the vertical motion of the projectile: the vertical position at time t is given by

where h is the initial height,

The total time of the fall is the time t at which y=0 (the projectile reaches the ground), so

Substituting into (1),

This can be re-arranged as

so we see that the initial height depends on the square of the horizontal distance travelled, d.

In this problem, one stands lands twice as far as the other stone does, so

d' = 2d

this means that the height of the taller builing is

so the taller building is 4 times taller than the smaller one.

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