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The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target the rifle must be aimed in order to hit the target
  • a)
    4.2 m
  • b)
    6.1 m
  • c)
    1.0 m
  • d)
    9.8 m
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
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.
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