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Rabbit's position vector (r) in the unit vector is 203.5î - 57j and the magnitude and directional angle of vector (r) are 195.35m and 0.004° respectively.
Given
x = 0.3t² + 7.2t + 28
y = 0.22t² - 9.1t +30
At t = 15s
x = 0.3(15)² + 7.2(15) +28 = 203.5
y = 0.22(15)² - 9.1(15) + 30 = -57
The rabbit's position vector (r) in unit vector notation is:
r = 203.5î - 57j
The magnitude of position vector (r)
r = √x² + y²
r = √(203.5)² - (57)² =√38163.25
= 195.35m
The directional angle of position vector (r)
tanθ = y/x = -57/203.5
θ = (-57/203.5)
θ = 0.004°
Hence, rabbit's position vector (r) in the unit vector is 203.5î - 57j and the magnitude and directional angle of vector (r) are 195.35m and 0.004° respectively.
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