A dart is thrown horizontally toward X at #25# #ms^-1# as shown in figure. It hits Y #0.12# #s# later. The distance XY is?

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1 Answer
David G.
Jun 27, 2017

#s_(XY)=0.07# #m# (#=7# #cm#)

Explanation:

Because we can consider the horizontal and vertical directions independently, this is actually exactly the same question as 'how far will an object, dropped from rest, fall in #0.12# #s#?'

The initial velocity in the horizontal, #x#, direction #u_x=25# #ms^-1#. This will stay constant, but we can ignore it.

The initial velocity in the vertical, #y#, direction is #u_y=0# #ms^-1#. Its acceleration will simply be the acceleration due to gravity, #a_y=9.8# #ms^-2#

#s_(XY)=u_yt+1/2a_yt^2=0xx0.12+1/2xx9.8xx0.12^2#

#s_(XY)=0.07# #m# (#=7# #cm#)

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