Distance Calculation Between Drone 1 and Drone 2
How far is drone 1 from drone 2 after the flight?
Final answer:
To find the distance between drone 1 and drone 2 after their flights, we can use the distance formula in three-dimensional space.
Explanation:
To find the distance between drone 1 and drone 2 after their flights, we can use the distance formula in three-dimensional space. The distance between two points in three-dimensional space (x1, y1, z1) and (x2, y2, z2) is given by: Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2). In this case, the positions of drone 1 and drone 2 are given as (3, -4, 0) and (6, 0, 5) respectively.
Substituting these values into the formula, we get: Distance = √((6 - 3)^2 + (0 - (-4))^2 + (5 - 0)^2).
Simplifying the expression, we have: Distance = √(3^2 + 4^2 + 5^2). Distance = √(9 + 16 + 25). Distance = √50. Therefore, the distance between drone 1 and drone 2 after their flights is approximately 7.07 meters.
Answer:
Using vectors and Cartesian coordinates, we calculate the displacement vector between Drone 1 and Drone 2. The magnitude of this displacement vector gives us the distance between the two drones, which is √50 meters.
Explanation:
The problem involves calculating the distance between two drones after they have traveled along specific vectors. In this problem, we use a Cartesian coordinate system with the unit vector i pointing east, the unit vector j pointing north, and the unit vector k pointing up from the ground. Drone 1's vector is ~r1= 3ˆi−4ˆj+ 0ˆk and Drone 2's vector is ~r2= 6ˆi+ 0ˆj+ 5ˆk.
To find the distance between the two drones, we need to calculate the difference of these vectors - the displacement vector: Δr = r2 - r1 = (6ˆi+ 0ˆj+ 5ˆk) - (3ˆi−4ˆj+ 0ˆk) = 3ˆi +4ˆj +5ˆk.
Finally, the magnitude of this displacement vector gives us the distance between the two drones: d = √(Δr · Δr) = √((3ˆi)^2 +(4ˆj)^2 + (5ˆk)^2) = √(9+16+25) = √50 meters.