A hunter with a gun of maximum range 200 meters tries to shoot a leopard sitting in a tree. The tree is at a distance of 100 m from the hunter and the leopard is sitting at a height of 2 m from the ground. In order to be able to hit the leopard
In order to hit the leopard, the hunter needs to consider the horizontal and vertical components of the shot.
1. Horizontal component:
The tree is 100 meters away from the hunter, and the maximum range of the gun is 200 meters. Since the tree is within range, the hunter can aim directly at the base of the tree.
2. Vertical component:
The leopard is sitting at a height of 2 meters from the ground. The hunter needs to calculate the angle at which to aim the gun to account for this height difference.
To do this, the hunter can use the concept of the tangent function:
tan(angle) = opposite / adjacent
In this case, the opposite side is the vertical distance from the ground to the leopard (2 meters) and the adjacent side is the horizontal distance from the hunter to the tree (100 meters).
tan(angle) = 2 / 100
To find the angle, the hunter can apply the inverse tangent function:
angle = arctan (2 / 100)
Using a scientific calculator or an online tool, the hunter can find the angle. In this case, the angle is approximately 1.14 degrees.
The hunter should aim the gun at the base of the tree (horizontally) and adjust the angle of the gun to approximately 1.14 degrees (vertically) to hit the leopard.
In order to hit the leopard, the hunter needs to aim at a specific point that will take into account both the horizontal distance to the tree and the vertical distance to the leopard. To calculate the angle at which the hunter should shoot, we can use trigonometry.
First, let's break down the problem:
- The horizontal distance from the hunter to the tree is given as 100 meters.
- The vertical distance from the hunter's position to the leopard's position is the sum of the leopard's height (2 meters) and the height of the tree.
To find the height of the tree, we can use the Pythagorean theorem:
(tree height)^2 = (distance to tree)^2 - (distance to leopard)^2
(tree height)^2 = 100^2 - 200^2
(tree height)^2 = 10000 - 40000
(tree height)^2 = -30000
Since the equation has a negative value, this means it is not possible for the leopard to be sitting on a tree with these given distances.
Therefore, it is not possible for the hunter to hit the leopard in this scenario.