Question

You are at home watching some old cartoons during Christmas break. Naturally, your mind wanders back to the happy times in physics class. You notice that Wiley Coyote chases the Road Runner. You estimate the Road Runner is about 94.5 cm tall, so then you estimate the Road Runner has about a 15.0 m head start and accelerates at about 2.75 m/s^2. Given this information, what is the smallest constant speed that Wiley Coyote has to run at to catch the Road Runner?

Answer 1

$$s_R=s_C\\s+0.5at^2=vt\\15+0.5(2.75)t^2=vt\\\frac{15}{t}+0.5(2.75)t=v\\\frac{dv}{dt}=0=-\frac{15}{t^2}+0.5(2.75)\to t=3.3\ s$$

Minimal constant speed:

$$v=\frac{15}{3.3}+0.5(2.75)(3.3)=9.08\frac{m}{s}$$