Problem Statement: In the war between McDonalds and Disney, Mickey Mouse throws a rock at Grimace. This is Disney, so nobody gets hurt, and the rock falls just short of Grimace's feet. In this problem, we want to find the total time that the rock was in the air, and the horizontal distance it traveled. Also, we want to find the tangential and normal components of acceleration once the rock has traveled a quarter of the way (talking about horizontal distance) to its final destination (i.e. Grimace's feet). Mickey Mouse and Grimace are standing at the same elevation on level ground. The rock leave's Mickey's hand at an elevation of 2 ft above the ground with a speed of 40 ft/sec at an angle of 18 above horizontal. Setting up domain: a) Draw a sketch of the problem and label the x-y coordinate system. Make the sketch as ridiculous as you like. I want to see lots of giant mutant bees. (0.5 pts) Distance time traveled by rock: b) How long does it take for the rock to just reach Grimace (just before it hits the ground)? You should get two times. How do you reason which time is correct? (1 pts) c) What is the relationship between the horizontal position and the time traveled? (0.5 pts) d) What was the total horizontal distance traveled by the rock before hitting the ground? What is a quarter of that horizontal distance? (1 pts) e) What was the time it took for the rock to reach a quarter of the total horizontal distance? (0.5 pts) Tangential and Normal Components of Acceleration: f) Draw the tangential and normal coordinates attached to the rock at the instance it has traveled a quarter of its total journey. (1 pts) g) Write down acceleration in component form (tangential and normal components). (0.5 pts) h) Write down the equation for the horizontal component of velocity of the rock. (0.5 pts) i) Write down the equation for the vertical component of velocity of the rock as a function of time. (0.5 pts) j) What is the speed of the rock as a function of time? Why do we need this? (2 pts) k) Write down the rock's y-component of position (elevation) as a function of the horizontal coordinate x. Hint, use part c) to express the elevation of the rock as a function of x. Why do we need to do this? (1 pts) 1) Find the tangential and normal components of acceleration at the instant the rock has traveled a quarter of its journey. (1 pts)