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A stone is dropped vertically from the top of a tower of height 40 m. At the same time a gun is aimed directly at the stone from the ground at horizontal distance 30 m from the base of the tower and fired. If the bullet from the gun is to hit the stone before it reaches the ground, the minimum velocity of the bullet must be, _________(m/sec) approximately.
Correct answer is '17.7'. Can you explain this answer?
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Verified Answer
A stone is dropped vertically from the top of a tower of height 40 m. ...
The initial y-coordinate of stone is 40 m and that it falls through a distance gun 
in a time t.
∴ y-coordinate of stone at any time after release is y =
Now y-coordinate for bullet at any time
when bullet hit the stone, y-coordinate for both one same
a collision will take place when
in a time t.∴ y-coordinate of stone at any time after release is y =
Now y-coordinate for bullet at any time
when bullet hit the stone, y-coordinate for both one same
a collision will take place when
Most Upvoted Answer
A stone is dropped vertically from the top of a tower of height 40 m. ...
Given:
- Height of the tower (h) = 40 m
- Horizontal distance from the base of the tower to the gun (d) = 30 m
Assumptions:
- There is no air resistance.
- The stone and bullet are dropped/fired at the same time.
Calculating the time taken by the stone to reach the ground:
- We can use the equation of motion: h = ut + (1/2)gt^2
- Where h is the height, u is the initial velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken.
- Since the stone is dropped, the initial velocity (u) will be 0 m/s. Plugging in the values, we get: 40 = 0*t + (1/2)*9.8*t^2
- Simplifying the equation, we get: 4.9*t^2 = 40
- Solving for t, we find: t = sqrt(40/4.9) ≈ 2.02 seconds
Calculating the horizontal distance covered by the stone in this time:
- We can use the equation of motion: distance = velocity * time
- Since the stone is dropped vertically, the horizontal distance covered will be 0 m.
Calculating the time taken by the bullet to reach the stone:
- The time taken by the bullet to reach the stone can be calculated using the horizontal distance and the relative velocity between the stone and the bullet.
- The relative velocity is the sum of the velocities of the stone and the bullet in the horizontal direction.
- Since the bullet is fired horizontally, its horizontal velocity will be its initial velocity.
- We need to find the minimum velocity of the bullet, so let's assume it is v m/s.
- The relative velocity between the stone and the bullet will be v - 0 = v m/s.
- Plugging in the values, we get: 30 = (v)(t)
- Substituting the value of t from earlier, we get: 30 = (v)(2.02)
- Solving for v, we find: v ≈ 14.85 m/s
Calculating the minimum velocity of the bullet:
- The minimum velocity of the bullet required to hit the stone before it reaches the ground is given by the relative velocity.
- From the calculation above, the relative velocity is approximately 14.85 m/s.
- Rounding this value to one decimal place, we get the minimum velocity of the bullet as approximately 14.9 m/s.
Explanation:
To hit the stone before it reaches the ground, the minimum velocity of the bullet must be approximately 14.9 m/s.
- Height of the tower (h) = 40 m
- Horizontal distance from the base of the tower to the gun (d) = 30 m
Assumptions:
- There is no air resistance.
- The stone and bullet are dropped/fired at the same time.
Calculating the time taken by the stone to reach the ground:
- We can use the equation of motion: h = ut + (1/2)gt^2
- Where h is the height, u is the initial velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken.
- Since the stone is dropped, the initial velocity (u) will be 0 m/s. Plugging in the values, we get: 40 = 0*t + (1/2)*9.8*t^2
- Simplifying the equation, we get: 4.9*t^2 = 40
- Solving for t, we find: t = sqrt(40/4.9) ≈ 2.02 seconds
Calculating the horizontal distance covered by the stone in this time:
- We can use the equation of motion: distance = velocity * time
- Since the stone is dropped vertically, the horizontal distance covered will be 0 m.
Calculating the time taken by the bullet to reach the stone:
- The time taken by the bullet to reach the stone can be calculated using the horizontal distance and the relative velocity between the stone and the bullet.
- The relative velocity is the sum of the velocities of the stone and the bullet in the horizontal direction.
- Since the bullet is fired horizontally, its horizontal velocity will be its initial velocity.
- We need to find the minimum velocity of the bullet, so let's assume it is v m/s.
- The relative velocity between the stone and the bullet will be v - 0 = v m/s.
- Plugging in the values, we get: 30 = (v)(t)
- Substituting the value of t from earlier, we get: 30 = (v)(2.02)
- Solving for v, we find: v ≈ 14.85 m/s
Calculating the minimum velocity of the bullet:
- The minimum velocity of the bullet required to hit the stone before it reaches the ground is given by the relative velocity.
- From the calculation above, the relative velocity is approximately 14.85 m/s.
- Rounding this value to one decimal place, we get the minimum velocity of the bullet as approximately 14.9 m/s.
Explanation:
To hit the stone before it reaches the ground, the minimum velocity of the bullet must be approximately 14.9 m/s.
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A stone is dropped vertically from the top of a tower of height 40 m. ...
Ok so u very nice
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A stone is dropped vertically from the top of a tower of height 40 m. At the same time a gun is aimed directly at the stone from the ground at horizontal distance 30 m from the base of the tower and fired. If the bullet from the gun is to hit the stone before it reaches the ground, the minimum velocity of the bullet must be, _________(m/sec) approximately.Correct answer is '17.7'. Can you explain this answer?
Question Description
A stone is dropped vertically from the top of a tower of height 40 m. At the same time a gun is aimed directly at the stone from the ground at horizontal distance 30 m from the base of the tower and fired. If the bullet from the gun is to hit the stone before it reaches the ground, the minimum velocity of the bullet must be, _________(m/sec) approximately.Correct answer is '17.7'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A stone is dropped vertically from the top of a tower of height 40 m. At the same time a gun is aimed directly at the stone from the ground at horizontal distance 30 m from the base of the tower and fired. If the bullet from the gun is to hit the stone before it reaches the ground, the minimum velocity of the bullet must be, _________(m/sec) approximately.Correct answer is '17.7'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is dropped vertically from the top of a tower of height 40 m. At the same time a gun is aimed directly at the stone from the ground at horizontal distance 30 m from the base of the tower and fired. If the bullet from the gun is to hit the stone before it reaches the ground, the minimum velocity of the bullet must be, _________(m/sec) approximately.Correct answer is '17.7'. Can you explain this answer?.
A stone is dropped vertically from the top of a tower of height 40 m. At the same time a gun is aimed directly at the stone from the ground at horizontal distance 30 m from the base of the tower and fired. If the bullet from the gun is to hit the stone before it reaches the ground, the minimum velocity of the bullet must be, _________(m/sec) approximately.Correct answer is '17.7'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A stone is dropped vertically from the top of a tower of height 40 m. At the same time a gun is aimed directly at the stone from the ground at horizontal distance 30 m from the base of the tower and fired. If the bullet from the gun is to hit the stone before it reaches the ground, the minimum velocity of the bullet must be, _________(m/sec) approximately.Correct answer is '17.7'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is dropped vertically from the top of a tower of height 40 m. At the same time a gun is aimed directly at the stone from the ground at horizontal distance 30 m from the base of the tower and fired. If the bullet from the gun is to hit the stone before it reaches the ground, the minimum velocity of the bullet must be, _________(m/sec) approximately.Correct answer is '17.7'. Can you explain this answer?.
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