(Scale: 1 cm = 50 4. An ambitious hiker walks 25 km North and 30 km East in a day. Find the hiker's resultant displacement. 5 km Use Tip-to-Tail Method)
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- In the control tower at a regional airport, an air traffic controller monitors two aircraft as their positions change with respect to the control tower. One plane is a cargo carrier Boeing 747 and the other plane is a Douglas DC-3. The Boeing is at an altitude of 2500 m, climbing at 100 above the horizontal, and moving 30 north of west. The DC-3 is at an altitude of 3000 m, climbing at 50 above the horizontal, and cruising directly west. (a) Find the position vectors of the planes relative to the control tower. (b) What is the distance between the planes at the moment the air traffic controller makes a note about their positions?A small plane flies at 200 km/h in still air. If the wind blows directly out of the west at 50 km/h, (a) in what direction must the pilot head her plane to move directly north across land and (b) how long does it take her to reach a point 300 km directly north of her starting point?Check Your Understanding Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, Indicate whether their velocity vectors are equal or otherwise. (a) Alice moves north at 6 knots and Bob moves west at 6 knots. (b) Alice moves west at 6 knots and Bob moves west a 3 knots. (C) Alice moves northeast at 6 knots and Bob moves south at 3 knots. (d) Alice moves northeast at 6 knots and Bob moves southwest a 6 knots. (e) Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.
- A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the following figure. Determine the east and north components of her displacement vector. How many more kilometers would she have to walk if she walked along the component displacements? What is her displacement vector?Can you sovle this and show steps? Also, what would the direction be of vector D x A (in terms of what)?What are the trig equations we use to find a vector's x and y components, and it's directional angle?
- Along distance commercial passenger plane flies North at 910km/h. At the same time, there is wind of 30 km/h from the West. Use ascaled diagram, Pythagorean Theorem and trigonometry to answer thefollowing. a) What is the magnitude of the resultant velocity? b) What isthe direction of the resultant (North, South, East, West, NE, NW, SE orSW). c). What is the angle of the resultant relative to due East? Roundyour answer to the nearest tenth.In the Superbowl, a quarterback throws a football while standing at the very center of the field on the 50 yard line. The ball leaves his hand at a height of 5 ft and has initial velocity of ~v(0) =< 40, 35, 32 > ft/sec. Assume an acceleration of 32 ft/sec2 due to gravity, i.e., ~a(t) =< 0, 0, −32 >, and that the vector ~i points down fieldtoward the endzone and that the vector ~j points to the sideline. The field is 150 ft in width and 300 ft in length.(a) Determine the position function that gives the position of the ball t seconds after it isthrown. (b) The ball is caught by a player 5 ft above the ground. Is the player in bounds or out ofbounds when he receives the ball? (Assume the player is standing vertically with bothtoes on the ground at the time of reception.)An object is shot horizontally off a cliff which is 19.95 meters high. The forward speed when it is fired is 6.321. How far forward from the firing point does it land? (Your answer should be in meters, but don't write the unit; just the nuumber.) Use the acceleration due to gravity near the earth's surface, g=10m/s^2 (Remember that the horizontal and vetical motion can be treated seperately, so you can first find the time of flight, then figure out how far foward it moves in that time)
- reverse the order of the twolegs of the walk; show that you get the same final result. Thatis, you first walk leg B , which is 20.0 m in a direction exactly40º south of west, and then leg A , which is 12.0 m in adirection exactly 20º west of north. (This problem shows thatA + B = B + A .)During her recent trip to the grocery store, Claire walked 14m,North to the end of an aisle. She then made a turn and walked 6m, 30o N of E. Finally, she made another turn and walked 8m, S. Determine the magnitude of Claire's resultant displacement and direction.Do not solve the full qn My question is why is the vector VAot = 1.5 and VAon =-2.6 as shown in the solution. I understand VAot is = -3cos30=-1.5 and VAon = -3sin30 =-2.6 Why is it postive 1.5 instead of negative 1.5 or for VAon why isit negative 2.6 and not positive 2.6? Why is Vb1t = -0.866 and not 0.866 and Vb1n = -0.5 and not 0.5. I dont get it how to visualise the vector direction. Please use a vector diagram with the angles to illustrate it.