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From the same point on level ground, two particles are launched…

Question

From the same point on level ground, two particles are launched simultaneously: the first straight up with speed 30 m/s, and the second at 30 m/s directed at 30 degrees above the horizontal. Taking g = 10 m/s^2 (both particles in the same vertical plane), find the distance between the two particles 2 seconds after launch (in metres).

✓ Verified answer: 60checked by our engine — not a guess

Step-by-step solution

Both particles experience the same gravitational acceleration, so their relative acceleration is zero and the separation grows linearly in time with the relative speed of the launch velocities.

The first velocity points 90 degrees above horizontal, the second 30 degrees, so the angle between them is 60 degrees, both magnitude 30 m/s.

Relative speed = sqrt(30^2 + 30^2 - 2*30*30 cos 60) = sqrt(900 + 900 - 900) = sqrt(900) = 30 m/s.
After 2 s the separation = 30*2 = 60 m.

Final answer60

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