Question

Two cars head in different directions. Car 1 averages 47.3 miles/hr on a direction of 225 degrees true, while car 2 averages 64.2 miles/ hr. After 2.50 hours it is known that they are 232 miles apart. Find the direction ( bearing that car 2 was headed, assuming that it was between 090 degrees true and 180 degrees true

Answer 1

Answer on Question #54209, Physics / Computational Physics

Two cars head in different directions. Car 1 averages 47.3 miles/hr on a direction of 225 degrees true, while car 2 averages 64.2 miles/ hr. After 2.50 hours it is known that they are 232 miles apart. Find the direction (bearing that car 2 was headed, assuming that it was between 090 degrees true and 180 degrees true

Solution:

I give the formula for the Law of Cosines and use it to find the missing angle.

$$c ^ {2} = a ^ {2} + b ^ {2} - 2 a b \cos \gamma$$

In our notations:

$$a = 4 7. 3 * 2. 5 0 = 1 1 8. 2 5 \text {m i l e s}$$ $$b = 6 4. 2 * 2. 5 0 = 1 6 0. 5 \text {m i l e s}$$ $$c = 2 3 2 \text {m i l e s}$$

Thus,

$$\cos \gamma = \frac {a ^ {2} + b ^ {2} - c ^ {2}}{2 a b} = \frac {1 1 8 . 2 5 ^ {2} + 1 6 0 . 5 ^ {2} - 2 3 2 ^ {2}}{2 * 1 1 8 . 5 * 1 6 0 . 5} = - 0. 3 7$$ $$\gamma = \cos^ {- 1} (- 0. 3 7) = 1 1 1. 7 ^ {\circ}$$ $$\theta = 2 2 5 ^ {\circ} - 1 1 1. 7 ^ {\circ} = 1 1 3. 3 ^ {\circ}$$

Answer: $113.3^{\circ}$