Vectors and Projectiles Legacy Problem #23 Guided Solution

This is a class of projectile problems known as a horizontally launched projectile problems. I know that because I'm told that I'm appealed throws the pumpkin horizontally. I have to pick up on cues in the problem such as words like horizontally. Now, I would recommend that as you approach this problem that you organize your information and provide an XY table that you see on this page. Create a table that looks something like that or print it out and use the table to organize information. What we know is that Ima is going to try to hit Mr. H's car, shame on her, and she's throwing it horizontally a distance of 13.4 meters from the base of the building. And so what we know is that DX equals 13.4 meters. It's not explicitly stated, but we also know about any projectile that AX is equal to 0 meters per second per second. So what we know about our XY table for the X column is two things, DX and AX. What we're eventually going to try to look for is VOX. That's the question. What's the horizontal speed that Ima must toss the pumpkin in order to get it to go this 13.4 meters? So our unknown here is DX. Now, in the Y column of the XY table, we know three things. The first thing we know is that the roof is 10.4 meters high, and so this pumpkin is going to fall a distance of 10.4 meters. We can say that DY equals negative 10.4 meters. And there's two other quantities that are not explicitly stated, but we know them. We know that VOY, the original Y velocity, is 0 meters per second. That will be the case always for the horizontally launched projectile problem. And finally, for any projectile problem, we know that AY equals negative 9.8 meters per second per second. So there's three bits of vertical information, and whenever you find three bits of information in any one of the columns, you can use those three bits of information to find a fourth and a fifth and a sixth, et cetera, bit of information. And the one that we would like to use is we would like to find the T. The reason we'd like to find the T is this problem eventually is going to ask us to calculate DX. In order to find DX, you need to know VOX and T. That's the DX equation. So since we don't have three bits of information on the left side, the XY column, we need to use the Y information to find the T. So I'll scan through my list of equations, and the one of great usefulness is the one that goes DY equals VOYT plus 1.5 AYT squared. I know DY, negative 10.4, so I plug it in. I know VOY is 0, so I plug that in. And I know AY, negative 9.8. The first term right side of the equation cancels out since VOY is 0, and the equation simplifies to negative 10.4 equal 1.5 times negative 9.8 times T squared. I can solve that one for T, and what I do, I get a value of T here of 1.4569. Now that I have that time value, I can use it to calculate the VOX value. I simply use the equation that DX equals VOX times T, and my DX here is given to me as 13.4 meters. My T I just calculated to be 1.4569 seconds, and I can combine those two bits of information in order to calculate the value for VOX.