VECTORS
2.7 A whale comes to the surface to breathe and then dives at an angle of 20.0° below the horizontal (Figure 2.7). If the whale continues in a straight line for 150 m, (a) how deep is it, and (b) how far has it travelled horizontally? (51m, 140m)
2.11 Vector points in the negative y direction and has a magnitude of 5 units. Vector has twice the magnitude and points in the positive x direction. Find the direction and magnitude of (a) (b) and (c) (11 units, -27°, 11 units, 207°, 11 units, 27°)
2.20 What is the direction and magnitude of your total displacement if you have travelled due west with a speed of 27 m/s for 130 s, then due south at 14 m/s for 62 s? (14° south of west, 3.6km)
2.21 A jogger runs with a speed of 3.25 m/s in a direction 30.0° above the x axis. (a) Find the x and y components of the jogger’s velocity. (b) How will the velocity components found in part (a) change if the jogger’s speed is halved? (2.81m/s, 1.63m/s)
2.22 You throw a ball upward with an initial speed of 4.5 m/s. When it returns to your hand 0.92 s later, it has the same speed in the downward direction (assuming air resistance can be ignored). What was the average acceleration vector of the ball? (-9.8m/s2, y direction)
2.23 A skateboarder rolls from rest down an inclined ramp that is 15.0 m long and inclined above the horizontal at an angle of When she reaches the bottom of the ramp 3.00 s later her speed is 10.0 m/s. Show that the average acceleration of the skateboarder is where (3.33m/s2, 3.36m/s2)
2.26 As an aeroplane taxies on the runway with a speed of 16.5 m/s, a flight attendant walks toward the tail of the plane with a speed of 1.22 m/s. What is the flight attendant’s speed relative to the ground? (15.3m/s)
2.27 As you hurry to catch your flight at the local airport, you encounter a moving walkway that is 85 m long and has a speed of 2.2 m/s relative to the ground. If it takes you 68 s to cover 85 m when walking on the ground, how long will it take you to cover the same distance on the walkway? Assume that you walk with the same speed on the walkway as you do on the ground. (25s)
2.28 The pilot of an aeroplane wishes to fly due north, but there is a 65 km/h wind blowing toward the east. (a) In what direction should the pilot head her plane if its speed relative to the air is 340 km/h? (b) Draw a vector diagram that illustrates your result in part (a). (c) If the pilot decreases the air speed of the plane, but still wants to head due north, should the angle found in part (a) be increased or decreased? (11° west of north)
2.29 A passenger walks from one side of a ferry to the other as it approaches a dock. If the passenger’s velocity is 1.50 m/s due north relative to the ferry, and 4.50 m/s at an angle of 30.0° west of north relative to the water, what are the direction and magnitude of the ferry’s velocity relative to the water? (43° west of north, 3.29m/s)
2.30 You are riding on a Jet Ski at an angle of 35° upstream on a river flowing with a speed of 2.8 m/s. If your velocity relative to the ground is 9.5 m/s at an angle of 20.0° upstream, what is the speed of the Jet Ski relative to the water? (11m/s)
2.32 Two people take identical Jet Skis across a river, travelling at the same speed relative to the water. Jet Ski A heads directly across the river and is carried downstream by the current before reaching the opposite shore. Jet Ski B travels in a direction that is 35° upstream and arrives at the opposite shore directly across from the starting point. (a) Which Jet Ski reaches the opposite shore in the least amount of time? (b) Confirm your answer to part (a) by finding the ratio of the time it takes for the two Jet Skis to cross the river. (0.82)