Note that because horizontal velocity is constant, on the horizontal table, v (^) f = v 0 , and a = 0. Also,
because the ball lands at essentially the same height it was launched from, Δx = 0 on the vertical table.
You should notice, too, that we rounded values in the tables to two significant figures (for example, we
said that v 0 in the vertical table equals 13 m/s, instead of 12.5 m/s). We can do this because the problem
is stated using only two significant figures for all values, so rounding to two digits is acceptable, and it
makes doing the math easier for us.
We know that t is the same in both tables—the ball stops moving horizontally at the same time that it
stops moving vertically (when it hits the ground). We have enough information in the vertical table to
solve for t by using equation .
Using this value for t , we can solve for x − x 0 in the horizontal direction, again using .
The cannonball traveled 57 m, about half the length of a football field.
You may have learned in your physics class that the range of a projectile (which is what we just
solved for) is
If you feel up to it, you can plug into this equation and show that you get the same answer we just got.
There’s no need to memorize the range equation, but it’s good to know the conceptual consequences of it:
the range of a projectile on level earth depends only on the initial speed and angle, and the maximum
range is when the angle is 45°.
A Final Word About Kinematics Charts
The more you practice kinematics problems using our table method, the better you’ll get at it, and the
quicker you’ll be able to solve these problems. Speed is important on the AP exam, and you can only gain