Is this possible? Baseball problem?

Question

We did a height function problem today which stated that a batter hit a baseball ball directly upward at an initial velocity of 96 ft/sec. We were to find the usual total time in air, max height, etc...all of which we did...

But one of my students vehemently argued that the "hit directly upward" was not even possible. Can anyone help clarify the reasonableness of this word problem?

Answer 1

I think your student was missing the point...the problem was an unrealistic, hypothetical problem designed to teach some fine points in physics. Hitting straight up is not impossible; if it were, we couldn't formulate physics relationships describing what happens with a straight up hit. But, and this is a big BUT, straight up is quite unlikely. The way I would put it...it's possible, but not feasible.

There are all sorts of real physics issues here that make hitting straight up unlikely. First, we are hitting in capricious air...full of currents and such. Second, the slightest spin on the ball would create a torque force that would pull the ball off its straight up path (that's where we get curve balls when pitching). Third, just how do we strike the ball so that the impact force is perfectly straight up (vertical) with the horizontal?

In the end, I'd preface such implausible problems with "If we could...." to emphasize the problem is unrealistic, but will demonstrate some laws or such of physics nonetheless. Physics classes in the lower levels are filled with simplifying assumptions, like no air drag, no friction, massless pendulums, etc., that make solving easier but are far from realistic. You can tell your student, just wait until the Masters level is reached...all those unrealistic, simplifying assumptions will disappear and he/she will wish they would come back.

Answer 2

Your question was only to illustrate a physics problem and in that context, whether or not it's possible to hit a ball straight up is irrelevant. Therefore, the problem is quite reasonable.

As to if it is or not, your student is wrong. It is possible for a batter to hit a ball straight up, though the chances against it are infinitesimally high. So many variables go into what can happen when bat meets ball. Direction of swing and incoming pitch, angle of contact, speed of pitch and swing, spin on the pitch, wind...among others. If you've watched a game, you've seen a pop-up caused by hitting a glancing blow on the underside of a ball. It never goes straight up because of some variable. But, if a perfectly flat pitch with no spin is met with a perfectly flat swing at precisely the correct angle, and with no outside force such as weather conditions to influence things, a ball could go exactly straight up.

Answer 3

"hit directly upward" is quite possible. Looking at the geometry of a bat (round) and a ball (also round), the collision of the ball with the bat can send the ball in any direction. Actually tryin to hit the ball directly upward, however, can be quite challenging. Its just like billiards. How one ball hits another and they both go off in different directions.

Answer 4

As a teacher, you already know that physics word problems are unrealistic; they exist to teach the students that the laws of physics are capable of predicting what we see out there in the observable universe, but motion in the real universe is complicated so we give them extremely simple situations (no friction or air resistance, for example, so any word problem with a baseball in it won't be remotely close to describing the actual motion) so that they can handle the math. So what I tell my students (university physics) is that, yes, these problems are unrealistic. They exist to give you practice at problem-solving and to set you up for bigger, better, more realistic problems later down the road.

Answer 5

it's not the point you were trying to solve.

Answer 6

You're the teacher. Why don't you tell us?