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Tiw stone are poject from the top of a tower 100m high each with the velocity of 20m/s. One is pojected vertically upwards and another vertically downwards. Calculate the time each stone takes to reach the ground and the velocity with which it strikes the ground.?
Most Upvoted Answer
Tiw stone are poject from the top of a tower 100m high each with the v...
PLZ FIRST CORRECT THE SPELLINGS
Stone projected vertically upward
height upto which it goes above(h) can be calculated as
v^2=u^2+2aS
v=0{final speed will be zero at the top}, a= negative{against gravity}
u^2=2aS
20�20= 2�10� h
h=20
total height from which it fall in the end= 100+20
=120
height travelled = ut + 1/2gt^2
120= 0+1/2�10t^2
t^2=24
t=2√6sec
v^2=u^2 +2a(total height)
v^2=0+ 2�10�120
v=20√6
stone projected vertically downward
v^2=u^2+2aH
v^2=20�20+ 2�10�100
=400+2000
=2400
v=20√6
v=u+gt
20√6=20+10t
2√6-2=t
Community Answer
Tiw stone are poject from the top of a tower 100m high each with the v...
Problem Statement: Two stones are projected from the top of a tower 100m high each with the velocity of 20m/s. One is projected vertically upwards and another vertically downwards. Calculate the time each stone takes to reach the ground and the velocity with which it strikes the ground.
Solution:
Given:
1. Time taken for the stone projected vertically upwards to reach the ground:
When a stone is projected vertically upwards, the initial velocity is in the upward direction and gravity acts in the downward direction. Hence, the acceleration (a) is -9.8m/s² (negative sign indicates that the acceleration is in the downward direction).
Using the equation of motion, we can find the time taken for the stone to reach the ground:
h = ut + 1/2at²
Where h is the height of the tower, u is the initial velocity, a is the acceleration and t is the time taken.
Substituting the given values, we get:
100 = 20t + 1/2(-9.8)t²
Simplifying the equation, we get:
4.9t² - 20t + 100 = 0
Using the quadratic formula, we get:
t = 4.04s (approx.)
Hence, the time taken for the stone projected vertically upwards to reach the ground is approximately 4.04 seconds.
2. Time taken for the stone projected vertically downwards to reach the ground:
When a stone is projected vertically downwards, the initial velocity is in the downward direction and gravity acts in the downward direction. Hence, the acceleration (a) is 9.8m/s² (positive sign indicates that the acceleration is in the downward direction).
Using the same equation of motion, we can find the time taken for the stone to reach the ground:
h = ut + 1/2at²
Where h is the height of the tower, u is the initial velocity, a is the acceleration and t is the time taken.
Substituting the given values, we get:
100 = -20t + 1/2(9.8)t²
Simplifying the equation, we get:
4.9t² + 20t + 100 = 0
Using the quadratic formula, we get:
t = 2.04s (approx.)
Hence, the time taken for the stone projected vertically downwards to reach the ground is approximately 2.04 seconds.
3. Velocity with which each stone strikes the ground:
When a stone falls freely under the influence of gravity, its final velocity (v) can be calculated using the following equation:
v² = u² + 2as
Where u is the initial velocity, a is the acceleration due to gravity and s is the distance fallen.
For the stone projected vertically upwards:
Since the stone is projected upwards with an initial velocity of 20m/s, its final velocity when it strikes the ground will be in the downward direction and its magnitude will be equal to the initial velocity. Hence, we can use the above equation to find the final
Solution:
Given:
- Height of the tower (h) = 100m
- Initial velocity (u) = 20m/s
1. Time taken for the stone projected vertically upwards to reach the ground:
When a stone is projected vertically upwards, the initial velocity is in the upward direction and gravity acts in the downward direction. Hence, the acceleration (a) is -9.8m/s² (negative sign indicates that the acceleration is in the downward direction).
Using the equation of motion, we can find the time taken for the stone to reach the ground:
h = ut + 1/2at²
Where h is the height of the tower, u is the initial velocity, a is the acceleration and t is the time taken.
Substituting the given values, we get:
100 = 20t + 1/2(-9.8)t²
Simplifying the equation, we get:
4.9t² - 20t + 100 = 0
Using the quadratic formula, we get:
t = 4.04s (approx.)
Hence, the time taken for the stone projected vertically upwards to reach the ground is approximately 4.04 seconds.
2. Time taken for the stone projected vertically downwards to reach the ground:
When a stone is projected vertically downwards, the initial velocity is in the downward direction and gravity acts in the downward direction. Hence, the acceleration (a) is 9.8m/s² (positive sign indicates that the acceleration is in the downward direction).
Using the same equation of motion, we can find the time taken for the stone to reach the ground:
h = ut + 1/2at²
Where h is the height of the tower, u is the initial velocity, a is the acceleration and t is the time taken.
Substituting the given values, we get:
100 = -20t + 1/2(9.8)t²
Simplifying the equation, we get:
4.9t² + 20t + 100 = 0
Using the quadratic formula, we get:
t = 2.04s (approx.)
Hence, the time taken for the stone projected vertically downwards to reach the ground is approximately 2.04 seconds.
3. Velocity with which each stone strikes the ground:
When a stone falls freely under the influence of gravity, its final velocity (v) can be calculated using the following equation:
v² = u² + 2as
Where u is the initial velocity, a is the acceleration due to gravity and s is the distance fallen.
For the stone projected vertically upwards:
Since the stone is projected upwards with an initial velocity of 20m/s, its final velocity when it strikes the ground will be in the downward direction and its magnitude will be equal to the initial velocity. Hence, we can use the above equation to find the final
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Tiw stone are poject from the top of a tower 100m high each with the velocity of 20m/s. One is pojected vertically upwards and another vertically downwards. Calculate the time each stone takes to reach the ground and the velocity with which it strikes the ground.?
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Tiw stone are poject from the top of a tower 100m high each with the velocity of 20m/s. One is pojected vertically upwards and another vertically downwards. Calculate the time each stone takes to reach the ground and the velocity with which it strikes the ground.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Tiw stone are poject from the top of a tower 100m high each with the velocity of 20m/s. One is pojected vertically upwards and another vertically downwards. Calculate the time each stone takes to reach the ground and the velocity with which it strikes the ground.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Tiw stone are poject from the top of a tower 100m high each with the velocity of 20m/s. One is pojected vertically upwards and another vertically downwards. Calculate the time each stone takes to reach the ground and the velocity with which it strikes the ground.?.
Tiw stone are poject from the top of a tower 100m high each with the velocity of 20m/s. One is pojected vertically upwards and another vertically downwards. Calculate the time each stone takes to reach the ground and the velocity with which it strikes the ground.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Tiw stone are poject from the top of a tower 100m high each with the velocity of 20m/s. One is pojected vertically upwards and another vertically downwards. Calculate the time each stone takes to reach the ground and the velocity with which it strikes the ground.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Tiw stone are poject from the top of a tower 100m high each with the velocity of 20m/s. One is pojected vertically upwards and another vertically downwards. Calculate the time each stone takes to reach the ground and the velocity with which it strikes the ground.?.
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