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A stone is dropped vertically from the top of a town of height 40 m. At the same time a gun is aimed directly at the stone from the ground at a 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 (m/sec) of the bullet must be approximately _____ .
Correct answer is '17-18'. Can you explain this answer?
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Verified Answer
A stone is dropped vertically from the top of a town of height 40 m. A...
To solve this question we will think about two cases
time taken by the stone to cover the x distance
and time taken by the bullet to reach the highest point
for case - II
vcosθ.t = 30
v = 17.7 m/sec
So minimum speed is 17.7 m/sec
time taken by the stone to cover the x distance
and time taken by the bullet to reach the highest point
for case - II
vcosθ.t = 30
v = 17.7 m/sec
So minimum speed is 17.7 m/sec
Most Upvoted Answer
A stone is dropped vertically from the top of a town of height 40 m. A...
Problem Statement: A stone is dropped vertically from the top of a town of height 40 m. At the same time a gun is aimed directly at the stone from the ground at a 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 (m/sec) of the bullet must be approximately _____ .
Solution:
To solve the problem, we need to find the minimum velocity of the bullet required to hit the stone before it reaches the ground. Let's break down the solution into the following steps:
Step 1: Calculate the time taken by the stone to reach the ground
Using the formula for time taken by an object dropped vertically, we can calculate the time taken by the stone to reach the ground.
t = sqrt(2h/g) where h is the height of the tower and g is the acceleration due to gravity.
t = sqrt(2*40/9.8) = 2 seconds (approx)
Step 2: Calculate the horizontal distance travelled by the stone in 2 seconds
Since the stone is dropped vertically, it only moves in the vertical direction. Therefore, the horizontal distance travelled by the stone in 2 seconds is 0.
Step 3: Calculate the vertical distance travelled by the stone in 1 second
Using the formula for distance travelled by an object under free fall, we can calculate the vertical distance travelled by the stone in 1 second.
s = 0.5*g*t^2 where t is the time taken by the stone to reach the ground.
s = 0.5*9.8*(2)^2 = 19.6 m
Therefore, the vertical distance travelled by the stone in 1 second is 19.6 m.
Step 4: Calculate the horizontal distance between the gun and the stone
Using the Pythagorean theorem, we can calculate the horizontal distance between the gun and the stone.
d = sqrt((40)^2 + (30)^2) = 50 m (approx)
Step 5: Calculate the time taken by the bullet to reach the stone
Since the bullet and the stone are supposed to meet at the same height and at the same time, the time taken by the bullet to reach the stone can be calculated as follows:
t = d/v where d is the horizontal distance between the gun and the stone and v is the velocity of the bullet.
t = 50/v
Step 6: Calculate the vertical distance travelled by the bullet in t seconds
Using the formula for distance travelled by an object under constant velocity, we can calculate the vertical distance travelled by the bullet in t seconds.
s = vt
Since the bullet and the stone are supposed to meet at the same height, the vertical distance travelled by the bullet in t seconds should be equal to 19.6 m.
s = 19.6
vt = 19.6
v = 19.6/t = 19.6/(50/v) = 0.392v
Therefore, the minimum velocity of the bullet required to hit the stone before it reaches the ground is approximately 0.392v.
Step 7: Calculate the minimum velocity of the bullet
To calculate the
Solution:
To solve the problem, we need to find the minimum velocity of the bullet required to hit the stone before it reaches the ground. Let's break down the solution into the following steps:
Step 1: Calculate the time taken by the stone to reach the ground
Using the formula for time taken by an object dropped vertically, we can calculate the time taken by the stone to reach the ground.
t = sqrt(2h/g) where h is the height of the tower and g is the acceleration due to gravity.
t = sqrt(2*40/9.8) = 2 seconds (approx)
Step 2: Calculate the horizontal distance travelled by the stone in 2 seconds
Since the stone is dropped vertically, it only moves in the vertical direction. Therefore, the horizontal distance travelled by the stone in 2 seconds is 0.
Step 3: Calculate the vertical distance travelled by the stone in 1 second
Using the formula for distance travelled by an object under free fall, we can calculate the vertical distance travelled by the stone in 1 second.
s = 0.5*g*t^2 where t is the time taken by the stone to reach the ground.
s = 0.5*9.8*(2)^2 = 19.6 m
Therefore, the vertical distance travelled by the stone in 1 second is 19.6 m.
Step 4: Calculate the horizontal distance between the gun and the stone
Using the Pythagorean theorem, we can calculate the horizontal distance between the gun and the stone.
d = sqrt((40)^2 + (30)^2) = 50 m (approx)
Step 5: Calculate the time taken by the bullet to reach the stone
Since the bullet and the stone are supposed to meet at the same height and at the same time, the time taken by the bullet to reach the stone can be calculated as follows:
t = d/v where d is the horizontal distance between the gun and the stone and v is the velocity of the bullet.
t = 50/v
Step 6: Calculate the vertical distance travelled by the bullet in t seconds
Using the formula for distance travelled by an object under constant velocity, we can calculate the vertical distance travelled by the bullet in t seconds.
s = vt
Since the bullet and the stone are supposed to meet at the same height, the vertical distance travelled by the bullet in t seconds should be equal to 19.6 m.
s = 19.6
vt = 19.6
v = 19.6/t = 19.6/(50/v) = 0.392v
Therefore, the minimum velocity of the bullet required to hit the stone before it reaches the ground is approximately 0.392v.
Step 7: Calculate the minimum velocity of the bullet
To calculate the
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A stone is dropped vertically from the top of a town of height 40 m. At the same time a gun is aimed directly at the stone from the ground at a 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 (m/sec) of the bullet must be approximately _____ .Correct answer is '17-18'. Can you explain this answer?
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A stone is dropped vertically from the top of a town of height 40 m. At the same time a gun is aimed directly at the stone from the ground at a 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 (m/sec) of the bullet must be approximately _____ .Correct answer is '17-18'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A stone is dropped vertically from the top of a town of height 40 m. At the same time a gun is aimed directly at the stone from the ground at a 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 (m/sec) of the bullet must be approximately _____ .Correct answer is '17-18'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is dropped vertically from the top of a town of height 40 m. At the same time a gun is aimed directly at the stone from the ground at a 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 (m/sec) of the bullet must be approximately _____ .Correct answer is '17-18'. Can you explain this answer?.
A stone is dropped vertically from the top of a town of height 40 m. At the same time a gun is aimed directly at the stone from the ground at a 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 (m/sec) of the bullet must be approximately _____ .Correct answer is '17-18'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A stone is dropped vertically from the top of a town of height 40 m. At the same time a gun is aimed directly at the stone from the ground at a 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 (m/sec) of the bullet must be approximately _____ .Correct answer is '17-18'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is dropped vertically from the top of a town of height 40 m. At the same time a gun is aimed directly at the stone from the ground at a 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 (m/sec) of the bullet must be approximately _____ .Correct answer is '17-18'. Can you explain this answer?.
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