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Vertically upward with a velocity of 20 m per second from the top of a multi stationery building the height of the point or ball is thrown is 25.0 m from the ground and b how long will it before the ball with the ground?
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Vertically upward with a velocity of 20 m per second from the top of a...
Understanding the Situation:
The situation described involves a ball being thrown vertically upward with an initial velocity of 20 m/s from the top of a building. The height of the building is given as 25.0 m from the ground. We need to calculate the time it will take for the ball to reach the ground.
Calculating Time to Reach Ground:
To calculate the time it will take for the ball to reach the ground, we can use the kinematic equation:
\[ s = ut + \frac{1}{2} at^2 \]
Where:
- \( s = -25.0 \) m (negative because the ball is moving downward)
- \( u = 20 \) m/s (initial velocity)
- \( a = -9.8 \) m/s\(^2\) (acceleration due to gravity, negative because it acts in the opposite direction to the initial velocity)
- \( t \) = time taken to reach the ground
Substituting the Values:
Substitute the given values into the equation:
\[ -25 = 20t + \frac{1}{2}(-9.8)t^2 \]
Simplify the equation to solve for \( t \):
\[ -25 = 20t - 4.9t^2 \]
\[ 4.9t^2 - 20t - 25 = 0 \]
Now, solve the quadratic equation to find the value of \( t \). The positive value will be the time taken for the ball to reach the ground.
Final Answer:
After solving the quadratic equation, we find that the time taken for the ball to reach the ground is approximately 2.04 seconds. Therefore, it will take about 2.04 seconds for the ball to reach the ground when thrown vertically upward from a building height of 25.0 meters.
The situation described involves a ball being thrown vertically upward with an initial velocity of 20 m/s from the top of a building. The height of the building is given as 25.0 m from the ground. We need to calculate the time it will take for the ball to reach the ground.
Calculating Time to Reach Ground:
To calculate the time it will take for the ball to reach the ground, we can use the kinematic equation:
\[ s = ut + \frac{1}{2} at^2 \]
Where:
- \( s = -25.0 \) m (negative because the ball is moving downward)
- \( u = 20 \) m/s (initial velocity)
- \( a = -9.8 \) m/s\(^2\) (acceleration due to gravity, negative because it acts in the opposite direction to the initial velocity)
- \( t \) = time taken to reach the ground
Substituting the Values:
Substitute the given values into the equation:
\[ -25 = 20t + \frac{1}{2}(-9.8)t^2 \]
Simplify the equation to solve for \( t \):
\[ -25 = 20t - 4.9t^2 \]
\[ 4.9t^2 - 20t - 25 = 0 \]
Now, solve the quadratic equation to find the value of \( t \). The positive value will be the time taken for the ball to reach the ground.
Final Answer:
After solving the quadratic equation, we find that the time taken for the ball to reach the ground is approximately 2.04 seconds. Therefore, it will take about 2.04 seconds for the ball to reach the ground when thrown vertically upward from a building height of 25.0 meters.
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Vertically upward with a velocity of 20 m per second from the top of a multi stationery building the height of the point or ball is thrown is 25.0 m from the ground and b how long will it before the ball with the ground?
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Vertically upward with a velocity of 20 m per second from the top of a multi stationery building the height of the point or ball is thrown is 25.0 m from the ground and b how long will it before the ball with the ground? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Vertically upward with a velocity of 20 m per second from the top of a multi stationery building the height of the point or ball is thrown is 25.0 m from the ground and b how long will it before the ball with the ground? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Vertically upward with a velocity of 20 m per second from the top of a multi stationery building the height of the point or ball is thrown is 25.0 m from the ground and b how long will it before the ball with the ground?.
Vertically upward with a velocity of 20 m per second from the top of a multi stationery building the height of the point or ball is thrown is 25.0 m from the ground and b how long will it before the ball with the ground? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Vertically upward with a velocity of 20 m per second from the top of a multi stationery building the height of the point or ball is thrown is 25.0 m from the ground and b how long will it before the ball with the ground? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Vertically upward with a velocity of 20 m per second from the top of a multi stationery building the height of the point or ball is thrown is 25.0 m from the ground and b how long will it before the ball with the ground?.
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