How to find the horizontal distance?

Can someone please explain to me how to do question 6a and b? Thanks!

1 Answer
A08
Dec 29, 2017

6 (a). There appears ambiguity in the text of the question.

Therefore, assume the stranded hiker is located at the ground level. We know that helicopter can stand still in the air. This is called Hovering.
As such helicopter can position itself just above the hiker to drop the package so that it lands next to him.

#=># Horizontal Distance between helicopter and hiker when package is dropped #=0" m"#

(b) Magnitude of vertical velocity #v# as the package hits the ground can be found from the following kinematic expression.

#v^2-u^2=2gh#
where #u# is initial velocity in the vertical direction and #=0#, #h# is height from which the package is dropped, and #g=9.81" ms"^-2#

As the package is dropped, it falls freely under the action of gravity. Inserting given values we get

#v^2-0^2=2xx9.81xx122.5#
#=>v=sqrt(2xx9.81xx122.5)#
#=>v=49.0" ms"^-1#, rounded to one decimal place.

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