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Grade 10Mechanics

A dart is thrown horizontally toward the bull's eye, point P on the dart board, with an initial speed of 10 m/s. It hits at point Q on the rim, vertically below P, 0.19 s later; see Fig. (a) What is the distance PQ? (b) How far away from the dart board did the player stand?
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

Profile image of Hrishant Goswami
11 Years agoGrade 10
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1 Answer

Profile image of Jitender Pal
11 Years ago
235-2164_1.PNG
The negative sign indicates the fact that the displacement is in the negative y direction.
Therefore the distance PQ is 0.17 m .
235-2471_1.PNG
Therefore, the horizontal separation between the dart board and the player is 1.9 m .