Question

Vc 2 m/s 40 m 30° 0,0 -х 15. (8 Points) Use the situation diagrammed above to answer the following questions. A swimmer crosses a river. Vs is the velocity of the swimmer relative to the water. Ve is the velocity of the rive with respect to the shore. (a) Find the x and y components of the swimmer's speed relative to the water (Vs). (b) Find the x and y components of the swimmer's speed relative to the shore (V (c) Find the magnitude and direction of the swimmer's velocity relative to the shore (V) (d) Find the time to cross the river and the distance the swimmer travels along the shore (X distance) (e) Find direction the swimmer would have to swim so he moves straight across the river, measured counterclockwise from the +x axis

Answer 1

(a) Given V_s = 5 m/s Resolve V_s in x and y direction we get, V_sx = V_s cos (30 degree) (-x) and V_sy = V_s sin (30 degree) (y) V_sx = (-4.33 x) m/s V_y = (2.5 y) m/s or, V_sx = -4.33 m/s and V_sy = 2.5 m/s (b) Velocity of the river is, V_c = (2x) m/s Velocity of swimmer is, (relative to water) V_s = (-4.33 x + 2.5 y) m/s Therefore Velocity of the swimmer relative to shore is, V = V_s - V_c = (-6.33 x + 2.5 y) m/s Implies V_cx = -6.33 m/s and V_cy = 2.5 m/s \r\n (c) Velocity of the swimmer relative to shore is, V = (-6.33 x + 2.5 y) m/s Therefore V = squareroot (6.33)^2 + (2.5)^2 m/s V = 6.81 m/s Direction = V/V = (-0.93 x + 0.37 y) (d) width of the river, y = 40 m y component of velocity of swimmer relative to shore is, V_y = 2.5 m/s Time to cross the river,