Can you help me get started with Problem #4 on the Major Quiz you handed out to us. A projectile leaves the edge of the table and falls freely a distance of 150 cm to the floor. It travels a horizontal distance of 6.1 cm during this fall. How long does it take to fall and what is its horizontal velocity during the fall?? I can't figure out where to plug the numbers in!!
First you have to take stock of what you've got:
For vertical motion let's choose downward as the positive direction. Then for the vertical motion you know that initial velocity is 0 and the acceleration is 980 cm/s^2, with a displacement of 150 cm (both acceleration and displacement are positive here, both being in the downward direction). So for vertical motion we know v0, a and `ds.
This means that we have enough informtion to solve the vertical motion for vf and `dt.
For the horizontal motion we know that `ds = 6.1 cm and acceleration is 0. Unless otherwise specified, we assume that horizontal forces are negligible so that horizontal acceleration must be 0. So for horizontal motion we know `ds and a.
Note that once we solve the vertical motion we will also know `dt, which is the same for both horizontal and vertical motion.
So we proceed to solve the vertical motion:
Knowing v0, a and `ds, we use the fourth equation of motion vf^2 = v0^2 + 2 a `ds to find vf. We get
vf = +- sqrt( v0^2 + 2 a `ds)
= +- sqrt( 0 ^ 2 + 2 * 980 cm/s^2 * 150 cm)
= +- sqrt( 294,000 cm^2 / s^2) = +-540 cm/s.
Knowing that the final velocity will be downward, which we recall was chosen as the positive direction, we discard the solution vf = - 540 cm/s and use the solution vf = +540 cm/s.
Since initial vertical velocity was 0 we conclude that the average vertical velocity is
vAve = (vf + v0) / 2 = (540 cm/s + 0 ) / 2 = 270 cm/s.
Vertical displacement was 150 cm, so we have
`dt = `ds / vAve = 150 cm / (270 cm/s) = .56 sec, approx..
Finally, knowing that `dt = .56 sec, we solve the horizontal motion. Recall that in the horizontal direction `ds is 6.1 cm and acceleration is a = 0. It follows that vf = v0, and vAve = vf = v0, so that
vAve = `ds / `dt = 6.1 cm / (.56 sec) = 11 cm/s, approx..