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Example: Finding the range of a projectile
For the previous example of the out of control bus which is forced to jump from a location ⟨0,40,−5⟩ with an initial velocity of ⟨80,7,−5⟩. We have now found the time of flight to be 9.59s and now want to find where the bus returns to the ground?
Facts
Lacking
Approximations & Assumptions
Representations
Solution
From the previous problem you already know the final location of the ball in the y direction to be 0 as it has met the ground after 9.59s.
Now to find the range in the x and z directions:
xf=xi+Vavg,xΔt
=0+80m/s(9.59s)
=767m
zf=zi+Vavg,zΔt
=−5+−5m/s(9.59s)
=−52.95
Final position = ⟨767,0,−52.95⟩ m