Question

A car was moving due to north with a velocity of 40 km per hour. In which direction
and with what speed the car will be moving, as seen from another car moving
towards east with a speed of 30 km per hour?

Answer 1

Answer on Question #50131, Physics, Mechanics | Kinematics | Dynamics

A car was moving due to north with a velocity of $40\mathrm{km}$ per hour. In which direction and with what speed the car will be moving, as seen from another car moving towards east with a speed of $30\mathrm{km}$ per hour?

Solution:

Relative motion from another car:

$$b = 3 0 \mathrm {k m} / \mathrm {h}$$ $$c ^ {2} = a ^ {2} + b ^ {2}$$ $$c = \sqrt {4 0 ^ {2} + 3 0 ^ {2}} = 5 0 \mathrm {k m / h}$$ $$\tan \theta = \frac {a}{b} = \frac {4 0}{3 0} = \frac {4}{3}$$ $$\theta = \tan^ {- 1} (4 / 3) = 5 3. 1 3 {}^ {\circ}$$

Answer: speed of car will be $50\mathrm{km / h}$ in a direction 53.13 degree north of west.

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