From point A (-10 m, 6 m) a particle starts moving with constant velocity of ? 2ˆi + 3ˆj ? m/s. Simultaneously from point B (7.5 m, -4 m), another particle starts moving with a constant velocity of ? −1.5ˆi + 5ˆj ? m/s. Find the time the particles travel before they collide.
Answers
Given : From point A (-10 m, 6 m) a particle starts moving with constant velocity of 2ˆi + 3ˆj m/s.
Simultaneously from point B (7.5 m, -4 m), another particle starts moving with a constant velocity of −1.5ˆi + 5ˆj m/s.
To Find : the time the particles travel before they collide.
Solution:
Let say the particles travel before they collide. for t secs
1st Particle
Initial Position = -10i + 6j
velocity 2ˆi + 3ˆj m/s.
Displacement = 2t i + 3t j
Final Position = -10i + 6j + 2t i + 3t j
= (2t - 10) i + (3t + 6) j
2nd Particle
Initial Position = 7.5i -4 j
velocity -15ˆi + 5ˆj m/s.
Displacement = -1.5t i + 5t j
Final Position = 7.5i -4 j -1.5t i + 5t j
= (-1.5t +7.5) i + (5t - 4) j
At time of collision , position would be same
(2t - 10) i + (3t + 6) j = (-1.5t +7.5) i + (5t - 4) j
=> 2t - 10 = -1.5t +7.5
=> 3.5t = 17.5
=> t = 5
or
3t + 6 = 5t - 4
=> 2t = 10
=> t = 5
Hence the time the particles travel before they collide is 5 secs
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