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A bird is flying from (3,4) to (5,6)with a speed of 20m/s find velocity vector of bird
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Introduction
To find the velocity vector of a bird flying from one point to another, we first need to determine the displacement vector and then divide it by the time taken to cover that distance.
1. Displacement Vector
- The bird is flying from the point A (3, 4) to point B (5, 6).
- The displacement vector D can be calculated using the formula:
D = B - A
= (5 - 3, 6 - 4)
= (2, 2).
2. Magnitude of Displacement
- The magnitude of the displacement vector can be found using the formula:
|D| = √(Δx² + Δy²)
where Δx = 2 and Δy = 2.
|D| = √(2² + 2²) = √8 = 2√2 m.
3. Time Taken
- To find the time taken, we use the speed of the bird:
Speed = Distance / Time
Rearranging gives us:
Time = Distance / Speed
= |D| / Speed = (2√2 m) / (20 m/s)
= √2 / 10 s.
4. Velocity Vector
- The velocity vector V can be calculated using the formula:
V = D / Time
Substituting the values:
V = (2, 2) / (√2 / 10)
= (2 * 10/√2, 2 * 10/√2)
= (20/√2, 20/√2)
= (10√2, 10√2) m/s.
Conclusion
The velocity vector of the bird flying from (3, 4) to (5, 6) is (10√2, 10√2) m/s. This vector indicates both the speed and direction of the bird’s flight.
To find the velocity vector of a bird flying from one point to another, we first need to determine the displacement vector and then divide it by the time taken to cover that distance.
1. Displacement Vector
- The bird is flying from the point A (3, 4) to point B (5, 6).
- The displacement vector D can be calculated using the formula:
D = B - A
= (5 - 3, 6 - 4)
= (2, 2).
2. Magnitude of Displacement
- The magnitude of the displacement vector can be found using the formula:
|D| = √(Δx² + Δy²)
where Δx = 2 and Δy = 2.
|D| = √(2² + 2²) = √8 = 2√2 m.
3. Time Taken
- To find the time taken, we use the speed of the bird:
Speed = Distance / Time
Rearranging gives us:
Time = Distance / Speed
= |D| / Speed = (2√2 m) / (20 m/s)
= √2 / 10 s.
4. Velocity Vector
- The velocity vector V can be calculated using the formula:
V = D / Time
Substituting the values:
V = (2, 2) / (√2 / 10)
= (2 * 10/√2, 2 * 10/√2)
= (20/√2, 20/√2)
= (10√2, 10√2) m/s.
Conclusion
The velocity vector of the bird flying from (3, 4) to (5, 6) is (10√2, 10√2) m/s. This vector indicates both the speed and direction of the bird’s flight.
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