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A ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45∘ with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball?
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A ball is projected from the ground at angle θ with the horizontal. Af...
- ***Given Information***
A ball is projected from the ground at an angle θ with the horizontal.
After 1 second, it is moving at an angle 45° with the horizontal.
After 2 seconds, it is moving horizontally.
- ***Analysis***
Let's break down the motion of the ball:
1. **Initial Projection**: When the ball is projected, it has a velocity V at an angle θ with the horizontal.
2. **1 second after projection**: The vertical component of the velocity decreases due to gravity, while the horizontal component remains the same. At this point, the velocity makes an angle of 45° with the horizontal.
3. **2 seconds after projection**: The vertical component of the velocity becomes zero, and the ball is moving horizontally.
- ***Calculations***
1. **Vertical Component of Velocity at 1 second**: V_y = Vsinθ - gt (where g is acceleration due to gravity)
2. **Horizontal Component of Velocity at 1 second**: V_x = Vcosθ
3. **At 1 second, the velocity makes an angle of 45° with the horizontal**: tan(45°) = V_y / V_x
4. **Using the above equations, we can solve for V and θ**.
- ***Final Answer***
By solving the equations, you can find the initial velocity of projection of the ball. This involves using trigonometric functions and kinematic equations to determine the values of V and θ that satisfy the given conditions.
A ball is projected from the ground at an angle θ with the horizontal.
After 1 second, it is moving at an angle 45° with the horizontal.
After 2 seconds, it is moving horizontally.
- ***Analysis***
Let's break down the motion of the ball:
1. **Initial Projection**: When the ball is projected, it has a velocity V at an angle θ with the horizontal.
2. **1 second after projection**: The vertical component of the velocity decreases due to gravity, while the horizontal component remains the same. At this point, the velocity makes an angle of 45° with the horizontal.
3. **2 seconds after projection**: The vertical component of the velocity becomes zero, and the ball is moving horizontally.
- ***Calculations***
1. **Vertical Component of Velocity at 1 second**: V_y = Vsinθ - gt (where g is acceleration due to gravity)
2. **Horizontal Component of Velocity at 1 second**: V_x = Vcosθ
3. **At 1 second, the velocity makes an angle of 45° with the horizontal**: tan(45°) = V_y / V_x
4. **Using the above equations, we can solve for V and θ**.
- ***Final Answer***
By solving the equations, you can find the initial velocity of projection of the ball. This involves using trigonometric functions and kinematic equations to determine the values of V and θ that satisfy the given conditions.
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A ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45∘ with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball?
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A ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45∘ with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45∘ with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45∘ with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball?.
A ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45∘ with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45∘ with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45∘ with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball?.
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