A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south. The two cars stick together after the collision. What is the direction of motion of the cars after collision?

Question

A  1500-kg car traveling at  90 km/h toward the east suddenly collides with a  3000-kg car traveling at  60 km/h toward the south. The two cars stick together after the collision. What is the direction of motion of the cars after collision?

Quizplus · Accepted Answer

To find the direction of motion after the collision, we use the conservation of momentum. The eastward momentum is $1500 \, \text{kg} \times 90 \, \text{km/h}$, and the southward momentum is $3000 \, \text{kg} \times 60 \, \text{km/h}$. Converting speeds to m/s (by dividing by 3.6), the eastward momentum is $37500 \, \text{kg} \cdot \text{m/s}$ and the southward momentum is $50000 \, \text{kg} \cdot \text{m/s}$. The angle $\theta$ with the east direction is given by $\tan(\theta) = \frac{50000}{37500}$, solving gives $\theta \approx 53.1^\circ$, so the direction is $53.1^\circ$ South of East.

A 1500-Kg Car Traveling at 90 Km/h Toward 53.1∘E of S53.1 ^ { \circ } \mathrm { E } \text { of } \mathrm { S }53.1∘E of S

A 1500-Kg Car Traveling at 90 Km/h Toward $53.1 ^ { \circ } \mathrm { E } \text { of } \mathrm { S }$