Vectors and Projectiles Legacy Problem #24 Guided Solution

A good problem solver has the habit of reading a problem carefully, looking for explicitly stated information as well as implied information, writing it down and organizing it, identifying the unknown variable, and then plotting out a strategy to get from known to unknown. For these horizontally launched projectile problems like this one, the strategy typically involves listing the given information in an XY table, such as the one that you see below this little audio help file, listing it in two columns, a column of known X information and a column of known Y information. So as I read through this problem about the cliff divers in Acapulco, I recognize that first of all, this is a horizontally launched projectile problem, and VOX is equal to zero. So in the X column I write VOX equals zero, and the reason I know VOX equals zero is because these are divers who are running off of a cliff, a horizontal cliff. And so originally there's no Y component. If there were a Y component, they probably would have listed an angle, as in an angled launch projectile problem, and they don't. The second thing I can find here is I can find that these cliff divers fall 45.1 meters. That's the first explicitly stated numerical value of the problem. That is a DY distance, a vertical distance. So in the Y column I write DY equals negative 45.1 meters. The second explicitly stated number is the 17.8 meters, and that's a horizontal distance that these cliff divers move horizontally. That's DX. So I write DX equals 17.8 meters. And now I know three bits of information. There are two more bits of information I can get out of this problem, and they're not explicitly stated. There's something that I know about all projectiles. This problem, in any projectile problem, the AX equals zero, that goes in the X column, and the AY equals negative 9.8 meters per second. So that completes what we know, and what we're looking for is we're looking for the value of VOX. Determine the speed with which Pedro must run off to find VOX. So the basic strategy for all of these horizontally launched projectile problems is to list the information and then look for three bits of either horizontal or vertical information. Typically those three pieces of information can be used to find a fourth and a fifth, and usually it's the time that you're looking for. After all, if we think about this problem, I want to find VOX. There's only one equation that has VOX in it, and it's the equation that goes DX equals VOX times T. If I know DX and I know T, I can find VOX. The only way to find the T is to use the three bits of Y information. So return to the set's overview page to look at the X and the Y equations, and you're looking for the one, the Y equation, that has in it DY, VOY, and AY, and T. That equation is DY equals VOYT plus one-half AYT squared. Now if I take my known information, I can put into it negative 45.1 for DY, VOY would be zero, and AY is negative 9.8. The fact that VOY is zero means that the first term on the right side of the equal sign cancels, and the equation becomes negative 45.1 equal one-half times negative 9.8 times T squared. You can take that information and use it to solve for T, and you'd get 3.0338 seconds. Take a deep breath, then return to the X column of your XY table, and use the equation DX equals VOX times T, where T is the number you just found, and DX is the 17.8 meters. That simple algebra you can now solve for VOX.