HUI nah-E'- ;' of a i\" \\ shame "': a? a Problem 2 A lifeguard is at the south hank ofa river owing from east to west at a speed thtw [see the gure}. A child at the north hank who is initially directly across the river from the lifeguard [a distance d away} falls into the river, and the lifeguard jumps in to save the child as quickly as possible. If the lifeguard's max swimming speed is V 3: aw in still water, then answer the following in terms of the quantities given [assume constant velocity}: a} Say that the moment the child falls into the river coincides with the moment the lifeguard jumps into the river to save them. At what angle must the lifeguard swim to save the child as quickly as possible? What total distance must the lifeguard travel to save the child? What is the time it takes until the child is rescued? h} Let's sag,r that the child has already oated a distance an]. to the west of the initial point where the child initially fell into the river until the lifeguard notices and begins swimming to save them. At what angle must the lifeguard swim at to save the child as quickly as possible? What is the time it takes until the child is rescued? How far to the west will the child be when the lifeguard reaches them? Problem 3 A head rolls on the ground towards the left at an initial speed of 2 cmf's when it is initially 10 cm to the right of a line that you decide to he the origin of your coordinate system. Ifthe head is accelerating at l cmlfs2 to the left write down the kinematic equations for the head and plot the acceleration of the head vs. time, velocity of the head vs. time, and position of the head vs. time. When does the head cross the line?I