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A bullet is fired from a gun with a speed of 1000 m/s in order to hit a target 100 m away. At what height above the target should the gun be aimed? (The resistance of air is negligible and g = 10 m/s2) [1995]
- a)5 cm
- b)10 cm
- c)15 cm
- d)20 cm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A bullet is fired from a gun with a speed of 1000 m/s in order to hit ...
Speed of the bullet (v) = 1000 m/s and horizontal distance of the target (s) = 100 m.
Time taken to cover the horizontal distance
Time taken to cover the horizontal distance
During this time, the bullet will fall down vertically due to gravitational acceleration.
Most Upvoted Answer
A bullet is fired from a gun with a speed of 1000 m/s in order to hit ...
To solve this problem, we can use the equations of motion in two dimensions. We need to find the height above the target at which the gun should be aimed so that the bullet hits the target 100 m away.
Let's assume the initial velocity of the bullet is v₀ = 1000 m/s and the distance to the target is d = 100 m. We also know that the acceleration due to gravity is g = 10 m/s².
1. Finding the time of flight:
The time taken for the bullet to reach the target can be found using the equation:
d = v₀t + (1/2)gt²
Substituting the given values:
100 = 1000t + (1/2)(10)t²
Simplifying the equation:
5t² + 100t - 100 = 0
Solving this quadratic equation, we get:
t = (-100 ± √(100² - 4(5)(-100)))/(2(5))
t = (-100 ± √(10000 + 2000))/10
t = (-100 ± √12000)/10
t = (-100 ± 109.54)/10
Taking the positive value, t = 0.954 s (approximately)
2. Finding the vertical distance:
The vertical distance traveled by the bullet can be calculated using the equation:
h = (1/2)gt²
Substituting the values:
h = (1/2)(10)(0.954)²
h = 4.572 m
3. Converting the height to centimeters:
Since the options are given in centimeters, we convert the height to centimeters:
4.572 m = 457.2 cm
Therefore, the gun should be aimed at a height of 5 cm above the target for the bullet to hit the target 100 m away.
Let's assume the initial velocity of the bullet is v₀ = 1000 m/s and the distance to the target is d = 100 m. We also know that the acceleration due to gravity is g = 10 m/s².
1. Finding the time of flight:
The time taken for the bullet to reach the target can be found using the equation:
d = v₀t + (1/2)gt²
Substituting the given values:
100 = 1000t + (1/2)(10)t²
Simplifying the equation:
5t² + 100t - 100 = 0
Solving this quadratic equation, we get:
t = (-100 ± √(100² - 4(5)(-100)))/(2(5))
t = (-100 ± √(10000 + 2000))/10
t = (-100 ± √12000)/10
t = (-100 ± 109.54)/10
Taking the positive value, t = 0.954 s (approximately)
2. Finding the vertical distance:
The vertical distance traveled by the bullet can be calculated using the equation:
h = (1/2)gt²
Substituting the values:
h = (1/2)(10)(0.954)²
h = 4.572 m
3. Converting the height to centimeters:
Since the options are given in centimeters, we convert the height to centimeters:
4.572 m = 457.2 cm
Therefore, the gun should be aimed at a height of 5 cm above the target for the bullet to hit the target 100 m away.
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A bullet is fired from a gun with a speed of 1000 m/s in order to hit a target 100 m away. At what height above the target should the gun be aimed? (The resistance of air is negligible and g = 10 m/s2) [1995]a)5 cmb)10 cmc)15 cmd)20 cmCorrect answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A bullet is fired from a gun with a speed of 1000 m/s in order to hit a target 100 m away. At what height above the target should the gun be aimed? (The resistance of air is negligible and g = 10 m/s2) [1995]a)5 cmb)10 cmc)15 cmd)20 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bullet is fired from a gun with a speed of 1000 m/s in order to hit a target 100 m away. At what height above the target should the gun be aimed? (The resistance of air is negligible and g = 10 m/s2) [1995]a)5 cmb)10 cmc)15 cmd)20 cmCorrect answer is option 'A'. Can you explain this answer?.
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