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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 $\langle 0,40,-5 \rangle$ with an initial velocity of $\langle 80,7,-5 \rangle$. 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:
$$ x_f = x_i + V_{avg,x} \Delta{t}$$
$$ = 0 + 80m/s(9.59s)$$ $$ = 767m$$
$$ z_f = z_i + V_{avg,z} \Delta{t}$$
$$ = -5 + -5m/s(9.59s)$$
$$ = -52.95$$
Final position = $\langle 767,0,-52.95 \rangle$ m