1. Problem-solving with Lorentz transformations. (a) (40 points) Solve Morin exercise 1.34 (p. 51) exclusively using Lorentz transformations; in other words, don't explicitly relate any lengths or times using length contraction or time dilation, since these will naturally be encoded in the Lorentz transformations. Solve the problem for a general car velocity v. You should find that there is a particular value of v for which the tree is at the same location in the ground frame as the eastward person: what is that velocity? Hint - there are 4 spacetime events: eastern person claps, western person claps, car passes western person, car passes tree. You will make your life easier by synchronizing the origins of the two coordinate systems to one of these events. (b) (20 points) You should find that your solution to part (a) is only a function of v2; in other words, the tree is at the same position whether or not the car is traveling eastward with velocity v or westward with velocity -v. Explain this fact in a few sentences, using a diagram. Hint: if the direction of the car is reversed, who claps first?1.34. Peopleclapping as: Two people stand a distance L apart along an eastwest road. They clap their hands simultaneously in the ground frame. You are driving eastward along this road at speed 4cf5. You notice that you are next to the western person at the same instant (as measured in your frame) that the eastern person claps. Later on, you notice that you are next to a tree at the same instant (as measured in your frame] that the western person claps. Where is the tree along the road'? (Describe its location in the ground frame.)