Concept explainers
Finding Velocity and Acceleration
(a) Kind the velocity vector, speed, and acceleration vector of the object.
(b) Evaluate the velocity vector and acceleration vector of the object at the given value of t.
Position Vector Time
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Multivariable Calculus
- Velocity of a Boat The boater in Exercise 63 wants to arrive at a point on the north shore of the river directly opposite the starting point In what direction should the boat be headed?arrow_forward3rd base resultant speed: απ || 2nd base A baseball is hit directly over second base with a velocity of 85 miles per hour. A wind of 22 miles per hour is blowing from third base to home. Describe the resultant speed and direction of the baseball. (Recall that the bases form a square.) Let a be the direction angle, the angle between the resultant velocity vector and the direction in which the baseball is hit. Home 1st base (Use decimal notation. Give your answer for the ball's speed to two decimal places. Give your answer for the ball's direction to the nearest degree. Include the degree symbol in your answer where needed.) miles per hourarrow_forwardThe position vector r describes the path of an object moving in space. (a) Find the velocity vector, speed, and acceleration vector of the object. (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. Position Vector r(t) = √ti + 5tj + 2t2k Time t = 4arrow_forward
- Another crosswind flight A model airplane is flying horizontally due east at 10 mi>hr when it encounters a horizontal crosswind blowing south at 5 mi/hr and an updraft blowing vertically upward at 5 mi/hr.a. Find the position vector that represents the velocity of the plane relative to the ground.b. Find the speed of the plane relative to the ground.arrow_forwardLinear algebra quesiton about direction vector intersecting a point.arrow_forwardThree-dimensional motion Consider the motion of the following objects. Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical and opposite g, the ground is horizontal, and only the gravitational force acts on the object unless otherwise stated.a. Find the velocity and position vectors, for t ≥ 0.b. Make a sketch of the trajectory.c. Determine the time of flight and range of the object.d. Determine the maximum height of the object. A soccer ball is kicked from the point ⟨0, 0, 0⟩ with an initialvelocity of ⟨0, 80, 80⟩ ft/s. The spin on the ball produces an accelerationof ⟨1.2, 0, 0⟩ ft/s2.arrow_forward
- Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical and opposite g, the ground is horizontal, and only the gravitational force acts on the object unless otherwise stated.a. Find the velocity and position vectors, for t ≥ 0.b. Make a sketch of the trajectory.c. Determine the time of flight and range of the object.d. Determine the maximum height of the object. A bullet is fired from a rifle 1 m above the ground in a northeastdirection. The initial velocity of the bullet is ⟨200, 200, 0⟩ m/s.arrow_forwardTrue Velocity of a Jet A jet is flying through a wind that is blowing with a speed of 55 mi/h in the direction N 30° E (see the figure).The jet has a speed of 765 mi/h relative to the air ,and the pilot heads the jet in the direction N 45° E. (a) Express the velocity of the wind as a vector in component form. (b) Express the velocity of the jet relative to the air as a vector in component form. (c) Find the true velocity of the jet as a vector. (d) Find the true speed and direction of the jet.arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage