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Find the magnitude of the vector sum

A + B.
Vector A is 85.0 m long in a 0° direction. Vector B is 101 m long in a 60° direction.​

User Sushruth
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Final answer:

To find the magnitude of the vector sum A + B, we can break down both vectors into x and y components. By using trigonometric identities, we can find the x and y components of vector B. Adding up the x and y components of both vectors will give us the x and y components of the vector sum. Finally, we can use the Pythagorean theorem to find the magnitude of the vector sum.

Step-by-step explanation:

To find the magnitude of the vector sum A + B, we need to break down both vectors into their x and y components. Vector A has a magnitude of 85 m and a direction of 0°, which means it only has an x-component. Vector B has a magnitude of 101 m and a direction of 60°. To find the x and y components of B, we can use the trigonometric identities: Bx = B * cos(θ) and By = B * sin(θ). Once we have the x and y components of both vectors, we can add them up to find the x and y components of the vector sum A + B. Finally, we can use the Pythagorean theorem to find the magnitude of the vector sum, which is the square root of the sum of the squares of the x and y components.

The x component of A is Ax = A * cos(θ) = 85 * cos(0°) = 85 * 1 = 85 m.

The x and y components of B are Bx = B * cos(θ) = 101 * cos(60°) = 50.5 m and By = B * sin(θ) = 101 * sin(60°) = 87.58 m.

The x and y components of A + B are Ax + Bx = 85 + 50.5 = 135.5 m and Ay + By = 0 + 87.58 = 87.58 m.

Using the Pythagorean theorem, the magnitude of A + B is |A + B| = sqrt((Ax + Bx)2 + (Ay + By)2) = sqrt((135.5)2 + (87.58)2) = sqrt(18339.5 + 7660.9364) = sqrt(25955.4364) = 161 m (rounded to 3 significant figures).

User Kufudo
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