PHYS 170 Worksheet 2.1 Solutions 1. A boat sails due North from a small island at 15 km/hr for 3 hours. It then turns 120° to the left and sails at 10 km/hr for 2 hours. It then turns 90° to the right and sails at 12 km/hr for 4 hours. A. Sketch, roughly to scale, the path of the boat. Label your diagram. 48 km @ 90° + 120° - 90€ 45 km @ 90° 20 km @ 90°+120° B. What is is the distance of the boat from the island at this time? The components of the first segment are 3 hr . 15- ? km ? cos 90° ? = 45 km · ? 0 ? hr ? sin 90° ? 1 ? The components of the second segment are ? km cos 210° ? ? -0.866 ? = 2 hr . 10 ? ? ? ? -0.500 ? ? -17.321 ? hr ? sin 210° ? = 20 km · ? ? -10.000 ? km The components of the third segment are km ? cos120° ? ? -0.500 ? ? -24.000 4 hr 012 --- 00 ? hr ? sin 120° ? = 48 km lg ? 0.866 ? ? 41.569 ? km ? ? ? ? ? 45 0 ? km . ? ? 0 ? ? -17.321 ? -24.000 ? ? ? -41.321 ? 1km The sum of the segments is [ 0+ ? = ? ? 45 ? ? -10.000 ? 0+0 ? 41.569 ? ? 76.569 ? So the distance from the island is (-41.321 ) + 76.5692 = 87.007 km C. What is the compass bearing of the boat relative to the island at this time? (North is up, which is +90° from the +x axis) A 76.569 = - 61.65°, but Ar is negative, so we need to add 180º -41.321 0 = tan 1 y = tan A X to get the angle from the x-axis of 118.4° (which looks right according to the figure). That is 118.4º- 90° = 28.4° to the left of North, which would be a bearing of -28.4º.
2. If the resultant FR of the two forces acting on the jet aircraft is to be directed along the positive x axis and have a magnitude of 10 kN, determine the angle 0 of the cable attached to the truck at B so that FB is a minimum. What is the magnitude of force in each cable when this occurs? C Fc 20° -x 0 A FB B It's smart to avoid re-writing numbers, so give them names: a = 20° Fy = 10 kN y force components must add to zero: F sina - Fp sin0 = 0 x force components must add to Fx : F cosa + Fp cos 0 = Fx sine Solve first equation for F in terms of Fp: Fc = FB sina sin 0 cos a + F cos 0 = Fx Plug F into second equation: F