moving so that its path has an angle of elevation of
![[Maple Math]](images/hwvec110.gif){kind=small}
. (a) Determine the angle of elevation which will maximize the number of meters from the base of the cliff that the object lands.
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.
>
(b) The kinetic energy of an object is given by
![[Maple Math]](images/hwvec111.gif)
, 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
![[Maple Math]](images/hwvec112.gif){kind=small}
, 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).
>