84. 4 relative velocity addition and accelerations Exercise 3: a boat must traverse a river 150 m wide. The river has a current of 3 km/h. and the boat can be rowed through the water with a uniform speed of 4 km/h Set up a convenient coordinate system, express the position vector of the boat at the time t assuming that the boat leaves the dock at the angle 0 with respect to a point moving with the water, as shown in fig.(b) Calculate 6 such that the boat lands at a point exactly opposite the starting point. How long will be the trip take? (a)Observer at O is fixed at shore (b)Observer at 0 is moving with water 84. 4 relative velocity addition and accelerations Solution: The velocity of the boat and water W =(4 km/h)cos i+(4 km/h )sin 8 j wG=3km/hi v=卩.+卩 I(4km/h)cos 8+3i+(4 km/h)sin 8 j The position of the boat as seen by the observer on the dock: IG =w +Ig I(4 cos 8+3ti+4 sin 0t j12 Exercise 3: A boat must traverse a river 150 m wide. The river has a current of 3 km/h, and the boat can be rowed through the water with a uniform speed of 4 km/h. Set up a convenient coordinate system, express the position vector of the boat at the time t , assuming that the boat leaves the dock at the angle θ with respect to a point moving with the water, as shown in fig. (b). Calculate θ such that the boat lands at a point exactly opposite the starting point. How long will be the trip take? (a) Observer at O is fixed at shore (b) Observer at O’ is moving with water §4.4 relative velocity addition and accelerations Solution: i j v v v v i v i j bG bw wG wG bw ˆ (4 km/h)sin ˆ [( 4km/h)cos 3] ˆ 3km/h ˆ (4 km/h)sin ˆ ( 4 km/h)cos θ θ θ θ = − + + = + = = − + r r r r r ti t j r r r bG bw wG ˆ 4 sin ˆ = [(−4cosθ + 3] + θ = + r r r The position of the boat as seen by the observer on the dock: The velocity of the boat and water §4.4 relative velocity addition and accelerations