Question

KC4014 Dynamics - Seminar Sheet 22 1) A particle is projected from point O on level ground with a speed U at an angle a to the horizontal. The particle lands on level ground. Neglecting aerodynamic drag, use the conservation of the energy to set up the equations of motion. Establish that the particle achieves a maximum height of U2 sin-(a) 2

Answer 1

Gravitational acceleration = g

Initial speed of the particle = U

Angle made with the horizontal = $\alpha$

Initial horizontal speed of the particle = UCos$\alpha$

Initial vertical speed of the particle = USin$\alpha$

The horizontal speed of the particle doesn't change as there is no force acting in the horizontal direction.

The vertical speed at maximum height becomes zero.

Horizontal speed of the particle at maximum height = UCos$\alpha$

Vertical speed of the particle at maximum height = 0

Speed of the particle at maximum height = UCos$\alpha$

Maximum height reached by the particle = H

By energy balance the initial kinetic energy is equal to the potential energy gained plus the kinetic energy at the top.

muz

(UCosa)

U2(1 - Cos a)

U2 Sina