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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?
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
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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
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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?.
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