Classical Mechanics Level 3

A uniform electric field \(\vec{E}\) exists at an angle \(\theta\) with respect to the ground. A particle of mass \(m\) and charge \(q\) is projected from the ground along the direction of the electric field with an initial velocity \(\vec{v}\).

If the coefficient of restitution between the particle and the ground is \(e\), find the distance travelled by the particle between the first and second impacts with the ground.

Details & Assumptions:

  1. \(|\vec{E}| = 15 NC^{-1}\)
  2. \(\theta = 30^{\circ}\)
  3. \(m = 3 kg\)
  4. \(q = 2 C\)
  5. \(|\vec{v}| = 20 ms^{-1}\)
  6. \(e = 0.5\)

Assume the gravitational field is uniform. Take \(g = 10 ms^{-2}\).


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