A rifle is used to shoot twice at a target, using identical cartridges. The first time, the rifle is aimed parallel to the ground and directly at the center of the bull's eye. The bullet strikes the target at a distance of HA below the center, however. The second time, the rifle is similarly aimed, but from 3.5 times the distance from the target. This time the bullet strikes the target a distance of HB below the center. Find the ratio of HB/HA.
hopefully it is in meters
To solve this problem, let's consider the first shot. We are given that the bullet strikes the target at a distance of HA below the center.
Now, let's move on to the second shot. The rifle is aimed parallel to the ground and from 3.5 times the distance from the target. This means that the rifle is aimed from a height of 3.5*HA above the center of the bull's eye.
Since the bullet is aimed parallel to the ground, the bullet follows a projectile path and its trajectory can be described by a parabola.
Now, let's find the ratio of HB/HA. To do this, we need to determine the ratio of the vertical distances traveled by the bullet in both shots.
The vertical distance traveled by the bullet in the first shot (HA) is equal to the vertical distance traveled by the bullet in the second shot (HB) plus 3.5*HA.
HA = HB + 3.5*HA
Subtract 3.5*HA from both sides of the equation:
HA - 3.5*HA = HB
Combine like terms:
-2.5*HA = HB
Finally, divide both sides of the equation by -2.5*HA:
HB/HA = -2.5
Therefore, the ratio of HB/HA is -2.5.
To find the ratio of HB/HA, we need to analyze the situation and determine the relationship between the two distances.
Let's denote the distance between the rifle and the target as D and the distance below the center of the bull's eye as H. We are given two scenarios:
1. In the first shot, the bullet strikes the target a distance of HA below the center.
2. In the second shot, from 3.5 times the distance from the target, the bullet strikes the target a distance of HB below the center.
From the given information, we know that in both scenarios, the rifle is aimed parallel to the ground and directly at the center of the bull's eye. Therefore, the bullet should theoretically hit the target at the same vertical position (height) if the aim is not affected by external factors like wind or gravity.
Let's set up an equation to represent the situation:
For the first shot:
Distance below center of bull's eye (HA) = H
For the second shot:
Distance below center of bull's eye (HB) = H × 3.5
To find the ratio of HB/HA, we can directly substitute the expressions for HA and HB:
HB/HA = (H × 3.5) / H
Simplifying the expression, we find:
HB/HA = 3.5
Therefore, the ratio of HB to HA is 3.5.
assuming no air friction, the horizontal speed of the bullet is the same everywhere in the problem
therefore the time in B is twice as lng as in A
the bullet therefore falls 3.5 times as long
h = .5 g t^2
hA = .5 g t^2
hB = .5 g (3.5 t)^2
3.5^2 t^2/t^2 = 12.25 times as far