Determine an expression for the position vector of a particle that starts on the positive y axis at t=0 (i. e., at t=0, (x0,y0)=(0,r)) and subsequently moves with constant ω. express your answer in terms of r, ω, t, and unit vectors i^ and j^.

Water is siphoned from a large tank and discharges into the atmosphere through a 50-mm diameter tube. the end of the tube is b = 2.6 m below the tank bottom which is a = 6.7 m deep, and viscous effects are negligible. determine the maximum height h over which the water can be siphoned without cavitation occurring. atmospheric pressure is 101.4 kpa, and the water vapor pressure is 1.79 kpa (absolute). report your answer in meters to two decimal places.