Crossing the River? ?II.? (a) In which direction should the motorboat in head in order to reach a point on the opposite bank directly east from the starting point? (The boat’s speed relative to the water remains 4.2 m/s.) (b) What is the velocity of the boat relative to the earth? (c) How much lime is required to cross the river? Exercise: Crossing the River I.? A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.2 m/s due east. The river is 800 m wide. (a) What is his velocity (magnitude and direction) relative to the earth? (b) How much time is required to cross the river? (c) How far south of his starting point will he reach the opposite bank?
2.1 The Idea of Limits distance Average velocity = time = slope of secant line Secant line – the line between two points on a graph Sparky’s average speed if he goes 8 miles in the span of 2 hours. 8mi 2hrs4mph Ex. An acrobat swings from a rope. Her displacement at time t is given by 3sint. What is her average velocity on the following intervals distance3 π = 6 [0, 2 ] time π ¿π 1.9099 2 distance ¿3sin.5 [0, .5] time .5 ~ 2.8766 distanc3sin.1 [0, .1] time = .1 ~ 2.9950