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PhysicsClassical Physics

Is a Collision Elastic When They Stick Together? Asteroid Example

The two asteroids undergo a perfectly inelastic collision. Add their momentum components to find a combined speed of about 900 m/s at 12.8° toward the second asteroid’s incoming direction.

Question

Two asteroids merge when they collide. Asteroid 1 has mass 15 × 10³ kg and initial speed 770 m/s. Asteroid 2 has mass 20 × 10³ kg and initial speed 1020 m/s. The angle between their incoming velocity vectors is 20°. Determine the speed of the combined object and its direction relative to asteroid 1’s initial velocity.

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Evidence boundary

This answer uses the masses, speeds, 20° inter-velocity angle, and sticking condition in OpenStax University Physics Volume 1, Chapter 9, Problem 56. Only a relative direction is specified, so the selected y-axis is a coordinate convention rather than an added compass direction. External impulse during the brief collision is neglected. Extra calculator digits document the calculation and do not assert extra measurement precision.