Supposed instead, the bird had leaped with a displacement having an x-component of 32.7m and a y-component 23.4m . Find the magnitude and direction of the displacement vector.
To find the magnitude and direction of the displacement vector, you can use the Pythagorean theorem and trigonometry. Here's how you can do it step by step:
1. Draw a diagram representing the x and y components of the displacement vector. The x-component is 32.7m, and the y-component is 23.4m.
2. Use the Pythagorean theorem to calculate the magnitude of the displacement vector. The Pythagorean theorem states that the square of the magnitude of the hypotenuse (displacement vector) is equal to the sum of the squares of the other two sides (x and y components). So, you can use the formula:
magnitude^2 = x-component^2 + y-component^2
Plugging in the given values, you get:
magnitude^2 = (32.7m)^2 + (23.4m)^2
magnitude^2 = 1069.29m^2 + 547.56m^2
magnitude^2 = 1616.85m^2
Taking the square root of both sides, you get:
magnitude = sqrt(1616.85m^2)
magnitude ≈ 40.21m
Therefore, the magnitude of the displacement vector is approximately 40.21m.
3. Use trigonometry to calculate the direction of the displacement vector. You can use the formula:
angle = arctan(y-component / x-component)
Plugging in the given values, you get:
angle = arctan(23.4m / 32.7m)
angle ≈ 0.6297 radians
To convert this into degrees, multiply by 180/π:
angle ≈ 0.6297 * (180/π) ≈ 36.02 degrees
Therefore, the direction of the displacement vector is approximately 36.02 degrees.
So, the magnitude of the displacement vector is approximately 40.21m, and its direction is approximately 36.02 degrees.