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A projectile is launched in the x-y plane with initial speed v0. At the highest point of its path it splits into two identical fragments. Both fragments hit the ground at the same instant and stick where they land. Taking the launch point as the origin and R as the range the projectile would have had without the explosion, which of the following CANNOT be the pair of position vectors of the two fragments where they land?
- R/2 i, 3R/2 i
- 0 i, 2R i
- R i - R k, R i + R k
- 2R i + R/2 k, R i - R/2 k
Correct answer: 2R i + R/2 k, R i - R/2 k
Solution
Since the fragments are identical, their CM must land at (R, 0); the average of options 1, 2 and 3 gives (R, 0), but option 4 averages to (1.5R, 0), which is impossible.
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