A bullet is fired horizontally from a rifle at 300m/s from a cliff above a plain below. The bullter reaches the plain 6s later. (a) How high was the cliff? (b) How far from the cliff did the bullet reach the plain? (c) What was the bullet's speed when it reached the plain?
(a) How far can a body fall in 6 seconds? That will be the height, H, since the in initial vertical velocity component is zero.
(b) (Horizontal velocity componet) * 6 seconds
(c) Kinetic energy (1/2) M V^2 will have increased by M g H
V^2 therefore increases by 2 g H from the initial value. You don't need to know M
To solve this problem, we can use the equations of linear motion. Let's break down each part of the problem.
(a) How high was the cliff?
To determine the height of the cliff, we first need to find the time it takes for the bullet to reach the ground. We know that the horizontal speed of the bullet remains constant, and it covers a horizontal distance in 6 seconds. Therefore, the vertical distance traveled in 6 seconds will be the height of the cliff.
We can use the formula for vertical displacement with constant acceleration:
d = ut + (1/2)at²
In this case, the initial vertical velocity (u) is 0 because it starts horizontally. Acceleration due to gravity (a) is approximately 9.8 m/s². The total time (t) is 6 seconds. Plugging these values into the equation, we get:
d = (1/2) × 9.8 × 6²
d = 176.4 meters
Therefore, the height of the cliff is 176.4 meters.
(b) How far from the cliff did the bullet reach the plain?
Since the bullet is fired horizontally, the horizontal distance it travels is the same as the distance from the cliff.
Using the formula for horizontal distance:
d = v × t
Here, the horizontal velocity (v) is 300 m/s, and the time (t) taken is 6 seconds. Substituting the values:
d = 300 × 6
d = 1800 meters
Therefore, the bullet reaches a point 1800 meters away from the cliff.
(c) What was the bullet's speed when it reached the plain?
The bullet's speed remains the same horizontally because there are no horizontal forces acting upon it. So, the speed when it reaches the plain is still 300 m/s.
To summarize:
(a) The height of the cliff is 176.4 meters.
(b) The bullet reaches a point 1800 meters away from the cliff.
(c) The bullet's speed when it reaches the plain is still 300 m/s.