Question

QUESTION 2 A man can row a boat at 2 m/s in still water. He wishes to cross a 50-m-wide river to point B, 50 m downstream. If the river flows with a velocity of 2 m/s, determine the speed of the boat and the time needed to make the crossing 50 m 2 m/s A 50 m B T T T Arial 3 (12pt) • T ABC III

Answer 1

Answers:

• The speed of the boat = 2.8284 m/s
• The time needed to make the crossing = 25 seconds

Solution:

Vyt Voir Given :- DV boat in still water 2 m/s Velocity of Velocity of Miver Ė 2 m/s 3 Width o river 50m e Position destination afrom source (A)-50m A 5om T (tve) damis 12 m/s A ev bir svo 50 m Formula :- Relative velocity : Vb Y = Velocity of boat with respect to ground Upa velocity of river with respect to ground V blir - Velsliby 7 bont toith respect to live

N the velocity in Resolving I and Ĵ (vertors) Voir 50m A 1045 Note: The boat has to travel in 45° angle to reach 'B' from ☆ as it is a Squate Therefore :- Vb Vi Sin 45° Vcos cos 45 B Vy oi-2 Velo Vyt Vblo 2 cosoi - 2 Sinoj Substituting the valries in the formula V6 V6 Sinits ? - Veos45 ] - 27 +26857-2engj Equating and i component, we We have Vb sin uso - Vb cos 45° - Solving Equation [A] and [B] 1 СА) 2 los o -2-2 Sind [B]

Sinus slo as Sin45 - 0845 = 1 vi 2 Vb cos 45° Therefore Vb 2. o + 2los o 2 Smo - Vb - 2 r -2 +2 (coso - Sino - cosa Sino . Therefore [ca Now Squaring on both sides of expation [C] Closo - Sno)² = (10² Costo + Sineo -2 cosa smo we know that costo tsmo 2 Smo cos 0 - 320 Substituting we get sin 20 = 1 Sin2o=0 Therefore o = 0 ; Substituting Substituting o=0 in (A 2 Cosco) Cosol Vp Sin 450 212 sin 48 = 1 2 وا - √2

V6 = 252 2.8284 m/s Answer it The speed of the boat (46) = 2.8284015 Thus, the time required by the boat to travel from port Ä to 'B' is. time distance Speed Distance from A to B (SAB) = √ 50² +502 t = SAB 255 2,8284 Answer: -The time needed to make the crossing is 25 seconds. 50² +502