Question

Two asteroids collide and stick together. The first asteroid has a mass of 15×10^3 kg and is initially moving at 770 m/s. The second asteroid has a mass of 20×10^3 kg and is moving at 1020 m/s. Their initial velocities make an angle of 20° with respect to each other. What is the final speed and direction with respect to the velocity of the first asteroid?

a) 1485 m/s, 13°
b) 1256 m/s, 27°
c) 1367 m/s, 20°
d) 1542 m/s, 18°

Answer 1

To find the final speed and direction with respect to the velocity of the first asteroid after collision between two asteroids that stick together, use the law of conservation of momentum and the law of sines. The correct answer is option c) 1367 m/s, 20°.

Step-by-step explanation:

To find the final speed and direction with respect to the velocity of the first asteroid after the collision, we can use the concept of conservation of momentum. After the collision, the two asteroids stick together and move as one.

Using the law of conservation of momentum, we can write:
(mass of first asteroid × velocity of first asteroid) + (mass of second asteroid × velocity of second asteroid) = total mass × final velocity

Using the given values and the law of sines, we can solve for the final speed and direction. The correct answer is option c) 1367 m/s, 20°.