Vector Worksheet 3 Answers

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Vector Worksheet 3 Answers 1. A box is being pulled across the floor by a rope at an angle of 50o to the horizontal. The tension in the rope is 100 N. (a) Find Fh, the horizontal component of the force on the rope. 100 N Fv 50o Fh Fh 100 100 cos 50 = 100 Fh = 100 cos 50 = Fh = 64.2 N

1. A box is being pulled across the floor by a rope at an angle of 50o to the horizontal. The tension in the rope is 125 N. (b) Find Fv, the vertical component of the force on the rope. 100 N Fv 50o 64.2 N Fv 100 100 sin 50 = 100 Fv = 100 sin 50 = Fv = 76.6 N

2. A plane is flying with a speed of 200 m/s at a bearing of 60o. (a) Determine the eastward component of the velocity. 0o 60o 270o 90o 180o

2. A plane is flying with a speed of 200 m/s at a bearing of 60o. (a) Determine the eastward component of the velocity. 200 m/s 60o vn 30o ve ve 200 200 cos 30 = 200 ve = 200 cos 30 = ve = 173 m/s

2. A plane is flying with a speed of 200 m/s at a bearing of 60o. (b) Determine the northward component of the velocity. 200 m/s 60o vn 30o 173 m/s vn 200 200 sin 30 = 200 vn = 200 sin 30 = vn = 100 m/s

2. A plane is flying with a speed of 200 m/s at a bearing of 60o. (c) How far east has the plane flown in 10 seconds? 200 m/s 60o 100 m/s 30o 173 m/s d = v t de = ve t = ( 173 m/s )( 10 s ) de = 1730 m

3. A plane is flying at a speed of 500 km/hr at a bearing of 240o. Find the westward component of the plane’s velocity. 0o 270o 90o 30o 180o 500 km/hr at 240o

3. A plane is flying at a speed of 525 km/hr at a bearing of 240o. Find the westward component of the plane’s velocity. vw vw = 500 cos 240 ? 30o vw = - 250 m/s 60o vw 500 km/hr vw 500 vw 500 500 cos 30 = 500 sin 60 = 500 500 vw = 500 cos 30 vw = 500 sin 60 vw = 433 km/hr vw = 433 km/hr

4. A rope is tied to a box on the floor and is held at angle of 60o to the horizontal. The box has a mass of 6.0 kg. A force of 100 N is exerted on the box via the rope. (a) Determine the vertical component of the force. Fv 100 100 N Fv 100 sin 60 = 100 60o 6.0 kg Fh Fv = 100 sin 60 Fv = 87 N

4. A rope is tied to a box on the floor and is held at angle of 60o to the horizontal. The box has a mass of 6.0 kg. A force of 85 N is exerted on the box via the rope. (b) Does the box stay on the floor, or is it pulled off the floor by the force? (Compare weight with Fv ) Wt. = m g 100 N 87 N = ( 6.0 kg )( 9.8 m/s2 ) 60o Wt. = 59 N 6.0 kg Fh Fv > Wt. Box pulled off floor Wt.