Answer Happy

. A particle of mass m is projected from the Earth’s surface
with speed v0 and at an angle θ above the horizontal. Assume that
the gravitational acceleration is constant and has the absolute
value g. (a) Determine the dependence on time of the horizontal and
vertical components of velocity and position. Determine the time
thit when the particle hits the ground. [4] (b) Calculate the
kinetic energy T and the potential energy V that the particle has
at any time 0 ≤ t ≤ thit (assume that the potential energy is zero
at the ground level). [3] (c) Use energy conservation to show that,
at any time, the velocity of the particle is equal in magnitude to
the magnitude of the velocity it would acquire in falling freely to
that point from a height v 2 0 /(2g) above the Earth’s surface. [3]
(d) A ball is projected with the speed √ 2gh at an angle α to the
horizontal in a plane perpendicular to a vertical wall of height h
and at a horizontal distance 2h away. The gravitational
acceleration g is constant. Show that the ball will not pass over
the wall for any α (hint: first draw a schematic figure of this
setup)