The velocity of an airplane with respect to the ground is $2.00 \times 102 \mathrm{~m} / \mathrm{s}$ at an angle of 30.0 degrees NORTH of EAST. The velocity of the airplane with respect to the air is $1.50 \times 10^{2} \mathrm{~m} / \mathrm{s}$ at an angle of 60.0 degrees NORTH of EAST. What is the velocity of the air with respect to the ground?
A) $134 \mathrm{~m} / \mathrm{s}$ at 49 degrees SOUTH of EAST
B) $103 \mathrm{~m} / \mathrm{s}$ at 65 degrees NORTH of EAST
C) $103 \mathrm{~m} / \mathrm{s}$ at 17 degrees SOUTH of EAST
D) $134 \mathrm{~m} / \mathrm{s}$ at 17 degrees NORTH of EAST
E) $112 \mathrm{~m} / \mathrm{s}$ at 50 degrees NORTH of EAST

Question

Quizplus · Accepted Answer

The velocity of the air with respect to the ground can be found by subtracting the velocity of the airplane with respect to the air from the velocity of the airplane with respect to the ground, using vector subtraction. This involves breaking down the velocities into their north-south and east-west components, subtracting these components, and then calculating the magnitude and direction of the resulting vector. The correct calculation leads to a velocity of $103 \mathrm{~m} / \mathrm{s}$ at 17 degrees SOUTH of EAST.

The Velocity of an Airplane with Respect to the Ground 2.00×102 m/s2.00 \times 102 \mathrm{~m} / \mathrm{s}2.00×102 m/s

The Velocity of an Airplane with Respect to the Ground $2.00 \times 102 \mathrm{~m} / \mathrm{s}$