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A ball is projected with a velocity, 10 ms–1, at an angle of 60° with the vertical direction. Its speed at the highest point of its trajectory will be:
- a)5√3ms-1
- b)5 ms–1
- c)10 ms–1
- d)Zero
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A ball is projected with a velocity, 10 ms–1, at an angle of 60&...
Understanding the Problem
A ball is projected with an initial velocity of 10 m/s at an angle of 60° with the vertical. We need to determine its speed at the highest point of its trajectory.
Velocity Components
To analyze the motion, we can break down the initial velocity into its vertical and horizontal components.
- Vertical Component (Vy):
- Vy = 10 m/s * cos(60°)
- Vy = 10 m/s * 0.5
- Vy = 5 m/s
- Horizontal Component (Vx):
- Vx = 10 m/s * sin(60°)
- Vx = 10 m/s * (√3/2)
- Vx = 5√3 m/s
Motion at the Highest Point
At the highest point of its trajectory, the vertical component of the velocity becomes zero due to gravity acting against the upward motion. However, the horizontal component remains unchanged throughout the flight.
- Vertical Velocity (Vy) at Highest Point:
- Vy = 0 m/s
- Horizontal Velocity (Vx):
- Vx = 5√3 m/s
Calculating the Speed at Highest Point
The speed at the highest point is purely due to the horizontal component since the vertical component is zero.
- Total Speed (S):
- S = √(Vx² + Vy²)
- S = √((5√3)² + 0²)
- S = √(75)
- S = 5√3 m/s
Conclusion
Thus, the speed of the ball at the highest point of its trajectory is 5√3 m/s, confirming that the correct answer is option 'A'.
A ball is projected with an initial velocity of 10 m/s at an angle of 60° with the vertical. We need to determine its speed at the highest point of its trajectory.
Velocity Components
To analyze the motion, we can break down the initial velocity into its vertical and horizontal components.
- Vertical Component (Vy):
- Vy = 10 m/s * cos(60°)
- Vy = 10 m/s * 0.5
- Vy = 5 m/s
- Horizontal Component (Vx):
- Vx = 10 m/s * sin(60°)
- Vx = 10 m/s * (√3/2)
- Vx = 5√3 m/s
Motion at the Highest Point
At the highest point of its trajectory, the vertical component of the velocity becomes zero due to gravity acting against the upward motion. However, the horizontal component remains unchanged throughout the flight.
- Vertical Velocity (Vy) at Highest Point:
- Vy = 0 m/s
- Horizontal Velocity (Vx):
- Vx = 5√3 m/s
Calculating the Speed at Highest Point
The speed at the highest point is purely due to the horizontal component since the vertical component is zero.
- Total Speed (S):
- S = √(Vx² + Vy²)
- S = √((5√3)² + 0²)
- S = √(75)
- S = 5√3 m/s
Conclusion
Thus, the speed of the ball at the highest point of its trajectory is 5√3 m/s, confirming that the correct answer is option 'A'.
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Community Answer
A ball is projected with a velocity, 10 ms–1, at an angle of 60&...
At highest point only horizontal component of velocity remains ⇒ ux = u cosθ
ux = u cosθ = 10cos30°
= 5√3ms-1
ux = u cosθ = 10cos30°
= 5√3ms-1
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A ball is projected with a velocity, 10 ms–1, at an angle of 60° with the vertical direction. Its speed at the highest point of its trajectory will be: a)5√3ms-1b)5 ms–1c)10 ms–1d)ZeroCorrect answer is option 'A'. Can you explain this answer?
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