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Catch the AirplaneYou are performing a stunt for a new action movie. In this stunt, you get on a motorcycle and immediately start accelerating (from rest) at 5 m/s$^2$ down a dirt path, in order to reach the door on an "get-away" airplane, which has already begun to taxi. Down the path, 122 m in front of you, is a huge crater. You must reach the door so your crew can pull you inside before you fall into the crater. When you start accelerating on the motorcycle, the airplane's door is 25 m ahead of you, and the airplane is going 5 m/s, and accelerating at 2 m/s$^2$. Once you reach the the door, it takes you 10 m of travel to exactly match the motorcycle's speed and acceleration to that of the airplane (so you'll stay directly next to the door). It then takes exactly $1$ second for your crew to pull you through the door and into the airplane. Will you make it before you and the motorcyle fall into the crater? Will this stunt allow for any suspense for the audience? |

Group solutions work when someone suggests the next step toward this problem's solution.### Steps accepted thus far

- First, I would figure out the position of the motorcycle to be $x_m$ or $x_m=1/2(5)t^2$.
- Next, I'd find the position of the airplane to be $x_p=25+5t+1/2(2)t^2.$
- To find where the motorcycle and airplane (door) meet, set $x_m=x_p$.
- This will give $1/2(5)t^2=25+5t+1/2(2)t^2$.

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