1. The problem statement, all variables and given/known data Question: At the instant a dart is launched at a high velocity, a target (often a cardboard monkey) drops from a suspended position downrange from the launching device. Show that if the dart is aimed directly at the target, it will always strike the falling target. (use a specific set of numbers). Variables I decided to use: velocity (v1= 100m/s angle shot at = 45 degrees time = 10 seconds 2. Relevant equations d(t) = (v1cosx)t + (v1sinx)t - 1/2(g)(t)2 Therefore: Horizontal - x = (v1cosx)t) Vertical - y = (v1sinx)t - 1/2(g)(t)2 3. The attempt at a solution This is the start in the problem. I'm not exactly sure how I'm supposed to prove it. I started with finding the horizontal and vertical. Hor: x = (v1cosx)t) x = (100cos45)10 x = 707m Ver: y = (v1sinx)t - 1/2(g)(t)2 y = (100sin45)10 - 1/2(9.8)(10)2 y = 217m Finding distance travelled by dart: a2 + b2 = c2 7072 + 2172 = c2 c = 739.5m Finding distance travelled by cardboard monkey in 10 seconds: d = v/t d = 9.8 * 10 d = 98m Therefore, I know how far the monkey falls in 10 seconds and how far and high the dart ends up, but how do I prove that the dart and monkey come in contact. Unless of course I did something with the steps above and have everything wrong. Any help is appreciated. Thank you.