A girl pokes her finger a distance L= 5cm into a glass of water as shown in the diagram. You may approximate the girl's finger as a cylinder with a cross-sectional area of Af= 1cm2. The glass cup has a cross- sectional area of Ac= 100cm² and the water is H= 10cm deep before the girl pokes her finger in. Recall that the density of water is pw= 103kg/m³. a) What is the change in the height 4H of the water in the glass due to the girl dipping her finger in? b) What is the direction and magnitude of the buoyant force on the girl's finger? c) What is the change in the pressure APof the water at the bottom of the glass resulting from the girl poking her finger in? d) What is the magnitude of the downward force that the girl's finger exerts on the water? Show your work and/or justify your answer. e) If the girl lowered her finger into the water at a constant rate of v= 1cm/s, then how fast did the surface of the water rise during that time?