Express the follow situation as a vector in component form: a. A boat is traveling at a bearing of 260° at 35 mph. b. A plane is traveling at 300 mph as it begins to descend for landing at an angle of depression of 15°. c. A cart full of children is being pulled up a ramp at an angle of elevation of 3° with a force of 5 lbs. d. A rope is being horizontally pulled by a truck due west of a car stuck in a ditch with a force of 1600 lbs.

A ball is thrown at an angle of 60° to the ground. If the ball lands 90 meters away. What was the initial speed of the ball? You must solve this problem using concept of vectors.

2. Consider the vector quantity B = 13 N, 149⁰. (a) Without doing any calculation, what quadrant do you expect this vector to be in? Why? (b) Do you expect B, to be positive or negative? Do you expect B, to be positive or negative? (c) Calculate the a component B (d) Calculate the y component By (e) Use a Cartesian coordinate system to represent B as an arrow. Remember to label your axes and use an adequate scale.

A small plane is flying horizontally due east in calm air at 175 mi/hr when it is hit by a horizontal crosswind blowing northwest at 40 mi/hr and a 30 mi/hr updraft. Find the resulting speed of the plane and describe with a sketch the approximate direction of the velocity relative to the ground. Let the unit vectors i, j, and k point east, north, and upward, respectively. Begin by writing vectors describing the velocity of the plane, the crosswind, and the updraft. What is the position vector that represents the velocity of the plane relative to the ground? The vector is (Oi+ (Dj+ (O k. (Type exact answers, using radicals as needed.)

Find the magnitude and direction angle (in degrees) for the vector i = (4,8) || = 4√5 ✔ Enter an exact value (i.e. no rounding). 0 = Round to two decimal places as needed.

A plane is flying on a course of 060° in still air at a speed of 300 km hr-, when it passes a control tower, A. Using i and j as the unit vectors due east and due north respectively, express the position vector of the plane relative to the control tower in terms of t, the time in hours since passing A. The next control at which the plane must report, B, has a position 300-/3i + 150j relative to A. a b Show that, after 90 minutes of travel, the plane is 150 km away from B. Find the length of time that the plane is less than 150 km from B.