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A particle moves in x-y plane starting from the origin in a direction making 30° angle with x-axis. Distance covered by it is 5 m. what is the position vector of the particle.
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A particle moves in x-y plane starting from the origin in a direction ...
Initial velocity = u = 20 m/s
Final velocity = v = 0 [ at maximum height , v = 0 ]
Final velocity = v = 0 [ at maximum height , v = 0 ]
Acceleration due to gravity(g) in this case , is taken as negative.
This is because , when the direction of motion of object is opposite to "g" , then value of g is taken as -ve
This is because , when the direction of motion of object is opposite to "g" , then value of g is taken as -ve
hence ,
g = -9.8 m/s²
Let's use the formula :-
[h = height ]
v² -u² = 2gh
0² - 20² = 2*-9.8*h
-400 = -19.6h
h = -400/-19.6
= 20.408 m [ approximately ]
-400 = -19.6h
h = -400/-19.6
= 20.408 m [ approximately ]
Most Upvoted Answer
A particle moves in x-y plane starting from the origin in a direction ...
Distance is 5 cm
Angle = 30 degree
Two components are x = 5 cos 30 and y = 5 sin 30
5 cos 30 = 5 Root3/2
5 sin 30 = 5/2
Angle makes with x-axis
Therefore , position vector is = -5Root3/2 i cap + 5/2 j cap
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Community Answer
A particle moves in x-y plane starting from the origin in a direction ...
Understanding the Problem
When a stone is thrown upwards, it experiences a deceleration due to gravity until it reaches its maximum height. The initial velocity of the stone is given as 20 m/s.
Key Concepts
- Initial Velocity (u): 20 m/s
- Final Velocity (v) at maximum height: 0 m/s (the stone stops moving upwards)
- Acceleration (a): -9.81 m/s² (acceleration due to gravity, acting downwards)
Using the Equation of Motion
To find the maximum height (h) reached by the stone, we can use the following equation of motion:
v² = u² + 2as
Where:
- v = final velocity (0 m/s at the maximum height)
- u = initial velocity (20 m/s)
- a = acceleration (-9.81 m/s²)
- s = maximum height (h)
Calculating Maximum Height
Substituting the known values into the equation:
0 = (20)² + 2 * (-9.81) * h
This simplifies to:
0 = 400 - 19.62h
Rearranging gives:
19.62h = 400
Now, solving for h:
h = 400 / 19.62
h ≈ 20.40 m
Conclusion
The maximum height the stone will reach is approximately 20.40 m, which corresponds to option A.
This calculation illustrates the relationship between initial velocity, acceleration due to gravity, and the maximum height reached by a projectile.
When a stone is thrown upwards, it experiences a deceleration due to gravity until it reaches its maximum height. The initial velocity of the stone is given as 20 m/s.
Key Concepts
- Initial Velocity (u): 20 m/s
- Final Velocity (v) at maximum height: 0 m/s (the stone stops moving upwards)
- Acceleration (a): -9.81 m/s² (acceleration due to gravity, acting downwards)
Using the Equation of Motion
To find the maximum height (h) reached by the stone, we can use the following equation of motion:
v² = u² + 2as
Where:
- v = final velocity (0 m/s at the maximum height)
- u = initial velocity (20 m/s)
- a = acceleration (-9.81 m/s²)
- s = maximum height (h)
Calculating Maximum Height
Substituting the known values into the equation:
0 = (20)² + 2 * (-9.81) * h
This simplifies to:
0 = 400 - 19.62h
Rearranging gives:
19.62h = 400
Now, solving for h:
h = 400 / 19.62
h ≈ 20.40 m
Conclusion
The maximum height the stone will reach is approximately 20.40 m, which corresponds to option A.
This calculation illustrates the relationship between initial velocity, acceleration due to gravity, and the maximum height reached by a projectile.
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A particle moves in x-y plane starting from the origin in a direction making 30° angle with x-axis. Distance covered by it is 5 m. what is the position vector of the particle.a)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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