The initial speed of a bullet fired from a rifle is 630 m/s. The rifle...
Given data:
Initial speed of bullet, u = 630 m/s
Distance from rifle to target, d = 700 m
To find:
The height at which the rifle must be aimed above the centre of the target, h.
Assumptions:
1. The acceleration due to gravity, g = 9.8 m/s²
2. The target is at the same level as the rifle.
Solution:
Let us assume that the bullet travels for a time t before hitting the target. During this time, it covers a horizontal distance d and a vertical distance h.
1. Finding time of flight:
Using the horizontal distance formula, we can find the time of flight as:
d = ut + (1/2)at²
Substituting the given values, we get:
700 = 630t + (1/2)(9.8)t²
Simplifying the equation, we get:
4.9t² + 630t - 700 = 0
Solving the quadratic equation, we get:
t = 1.11 s (approx)
2. Finding height of rifle above the target:
Using the vertical distance formula, we can find the height of the rifle above the target as:
h = (1/2)gt²
Substituting the values of g and t, we get:
h = (1/2)(9.8)(1.11)²
h = 6.1 m (approx)
Therefore, the height at which the rifle must be aimed above the centre of the target is 6.1 m.
Answer: Option B) 6.1 m.