Wile E. Coyote (Genius!) is trying to catch the Roadrunner, as usual. Continuing

Question

Wile E. Coyote (Genius!) is trying to catch the Roadrunner, as usual. Continuing the rocket theme of the assignment so far, he has put on roller skates and strapped a large rocket to his back. At t = 0 Wile E. has not lit his rocket but is coasting along on his roller skates at 10 m/s when the Roadrunner passes him (Bee-Beep!) going at a constant 50.0 m/s. Wile E. lights his rocket just as the Roadrunner passes him and immediately starts to accelerate in pursuit of the Roadrunner at 30.0 m/s2. Write equations which express the position of the Roadrunner as a function of time and the position of Wile E. as a function of time. When does Wile E. match velocity with the Roadrunner? Where are both Wile E. and the Roadrunner at this time? When does Wile E. catch up with the Roadrunner? Just as Wile E. catches up with the Roadrunner his rocket runs out of fuel. As a result of the sudden change in the forces acting on him he loses his balance and falls over. He is now sliding along the road with an acceleration of 6.00 m/s2 pointed in the opposite direction to his motion. He misses grabbing the Roadrunner because of this. When is the next time that Wile E. will have an opportunity to grab the Roadrunner assuming that the Roadrunner continues moving in a straight line at a constant 50.0 m/s? Make up a non-uniformly accelerated motion. That is, make up an acceleration as a function of time. The criteria you should follow are: The acceleration must change.

Explanation / Answer

a) x roadrunner = 50 t

x wile = 10 t + 0.5*30*t^2 = 10 t + 15 t^2

b)

50 = 10 + 30 t

40 = 30 t

t = 4/3 = 1.33 s
c)

50 t = 10 t + 15 t^2

40 t = 15 t^2

t = 40/15 = 2.67 s

d)
v when reach = 10 + 30*2.67= 90 m/s

so x roadrunner = 50 t

x wile = 90 - 0.5*6*t^2 = 90-3 t^2

90 t- 3 t^2 = 50 t

40 t = 3 t^2
t = 40/3 = 13.3 s

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