332 Physics – Unit 2: Vectors and Projectile Motion Review

1) A banana is thrown upwards with a speed of 25m/s at 40 degrees. Determine the initial horizontal and vertical speeds of the tasty yellow fruit.

2) A boat travels along a river at 30m/s @ 30o north of west and a wind blows on the boat in a direction of 280o at 7m/s. If the current in the river is moves at 10m/s at 30 degrees north of east, find the resultant velocity of the boat with respect to the shore.

3) A stone is thrown horizontally at 20 m/s from the top of a cliff 63m high. Determine the resultant speed as the stone hits the ground.

4) A golfer takes 2 putts to sink a ball in the hole. The first putt displaces the ball 6m east, and the second displaces the ball 5.4m, 45o south of east. What displacement would have sunk the ball in 1 putt?

5) How far horizontally does a roller coaster move if it moves 41m up a ramp of 40o?

6) A swimmer swims north across a river that flows at 0.2m/s from west to east. If the speed of the swimmer is 0.15m/s relative to still water, what is the velocity of the swimmer relative to the earth?

7) In a 500m stretch of river, the speed of the current is a constant 5m/s. How long does it take a purple boat with white trim to finish a round trip (upstream and downstream) if the speed of the boat is 7.5m/s relative to still water?

8) The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h. At what distance d before the target should it release a heavy bomb to hit the target X?

9) An object is shot from the back of a truck moving at 30 mph on a straight horizontal road. The launcher is aimed upward, perpendicular to the bed of the truck. Where does the object land in relation to the truck? Neglect air resistance.

10) The vectors a, b, and c are related by c = a + b. Which diagram below illustrates this relationship?

11) Find the resultant of a 27m displacement vector at 0o and a 34m displacement when the angle between them is 118°.

12) You are riding in a boat that is traveling 15.0 m/s in still water. a) You walk from the front of the boat to the back at 3.0 m/s relative to the boat. What is your speed relative to the earth?

b) You now walk to the front of the boat at same speed as before, what is your speed relative to earth?

c) What if boat was moving north with a river current of 12m/s south while you walked towards back of boat at 3m/s relative to boat, what would be your speed relative to earth?

13) Starting at the origin, the following displacements are made in the xy-plane: 60 mm in the +y-direction, 30 mm in the x-direction, and 50 mm at 240°. Find the resultant displacement in mm.

14) A rock is projected horizontally from a very high cliff at a speed of 65m/s as shown. a) What is the resultant speed of the rock after it has fallen a vertical distance of 35 m? b) What is the acceleration of the rock after 2s of fall? c) What is the horizontal speed of the rock after 1s of fall? d) If the range of the rock is 320m, what is the height of the cliff?

15) The diagram at right shows the resultant vector R of adding vector 1 and vector 2. Which of the following represents the magnitude of the vertical component of vector 1? A. I B. II C. III D. IV

ANSWERS: 1) x= 19.2m/s, y = 16.1m/s, 2) 20.8m/s @ 140.8o 3) 40.3m/s 4) 10.5m @ -21.2o

o CA 5) 31.4m 6) 0.25m/s @ 36.9 7) 240s 8) 421m 9) Lands in the truck 10) II 11) 32m

BD 12) 12m/s, 18m/s, 0 13) 17.4mm @ 77.3o 14) 70.1m/s, -9.8m/s2, 65m/s, 118.7m 15) B