**Problem 8**

An projectile starts at the top of a 40 meter high vertical cliff with an initial speed of 100 meters per second,

moving so that its path has an angle of elevation of
.

(a) Determine the angle of elevation which will maximize the number of meters from the base of the cliff that the object lands.

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(b) The kinetic energy of an object is given by
, where
*m*
is the mass of the object and
*v*
is the velocity of the object. The potential energy of an object is given by
, where
*h*
is the height above zero, and
*g*
is the acceleration due to gravity. Determine the ratio
*EK*
/(
*EK+EP*
) at
*t*
=0 for the projectile
. Show that this ratio is the same as the square of the tangent of the angle that you found in part (a).

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