Stones are thrown horizontally, with the same initial velocity, from the tops of two different buildings, A and B. The stone from building A lands 4 times as far from the base of the building as does the stone from building B. What is the ratio of building A's height to building B's height?
A
C
A
B
To solve this problem, we need to analyze the horizontal motion of the stones. Since both stones are thrown horizontally with the same initial velocity, the only force acting on them is gravity in the vertical direction. This means that their horizontal velocities are the same.
Let's denote the horizontal distances traveled by the stones as dA and dB, and the heights of buildings A and B as hA and hB, respectively.
We are given that the stone from building A lands 4 times as far from the base of the building as the stone from building B:
dA = 4 * dB
Now, let's analyze the vertical motion of the stones. Since there are no horizontal forces acting on the stones, they will fall vertically due to gravity. In the absence of air resistance, the time of flight for both stones will be the same.
Using the kinematic equation for vertical motion:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity, and t is the time of flight.
For both stones, the time of flight will be the same because they are thrown with the same initial vertical velocity. Therefore, we can write:
hA = (1/2) * g * t^2
hB = (1/2) * g * t^2
Dividing the first equation by the second:
hA / hB = (1/2) * g * t^2 / (1/2) * g * t^2
Simplifying:
hA / hB = 1
Therefore, the ratio of building A's height to building B's height is 1.