III) Now consider an object moving across a river so that it has two velocities with respect to the land on the sides of the river, i) the velocity of the river current ii) the velocity it has as it moves across the river. Velocities are properly described as vectors. The river flows with a velocity of 3 m/s and the boat moves in a direction perpendicular to the river current with a velocity of 6 m/s. (a) Draw a diagram of this situation and show the velocity vectors for the flowing river water and the motion of the boat with respect to the water. Hint: First imagine that the boat moves across a still body of water and then start the water moving. (b) Find the total velocity of the boat with respect to the land on the sides of the river graphically and then by adding x and y components.

III) Now consider an object moving across a river so that it has two velocities with respect to the land on the sides of the river, i) the velocity of the river current ii) the velocity it has as it moves across the river. Velocities are properly described as vectors. The river flows with a velocity of 3 m/s and the boat moves in a direction perpendicular to the river current with a velocity of 6 m/s. (a) Draw a diagram of this situation and show the velocity vectors for the flowing river water and the motion of the boat with respect to the water. Hint: First imagine that the boat moves across a still body of water and then start the water moving. (b) Find the total velocity of the boat with respect to the land on the sides of the river graphically and then by adding x and y components.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter5: Trigonometric Functions: Right Triangle Approach

Section5.1: Angle Measure

Problem 4E: Object A is travelling along a circle of radius 2, and Object B is travelling along a circle of...

See similar textbooks

Similar questions

The second hand of a clock is 8 centimeters long. Find the linear speed of the tip of the second hand as it passes around the clock face.
Object A is travelling along a circle of radius 2, and Object B is travelling along a circle of radius 5. The object have the same angular speed. Do the objects have the same linear speed? If not, which object has the greater linear speed?
8) An airplane is on a heading of 065° at 350 km/h and an 75 km/h wind is blowing from 310°. Determine the resultant velocity of the airplane, using Cartesian vectors. Include a diagram(s) as part of your solution.
What is the unit vector in the direction of v = < - 5 , - 1 > ?
The current in a river is pushing a boat in direction 24 degree north of east with a speed of 16 km/hr. The wind is pushing the same boat in a direction 81 degree south of east with a speed of 7 km/hr. Find the velocity vector of the boat's engine (relative to the water) if the boat actually moves due east at a speed of 50 km/hr relative to the ground. Find the engine speed to push the boat and its direction.
Just explain thx
1) Find the component form of the vector that represents the velocity of an airplane descending at a speed of 100 miles per hour at angle of 15* below the horizontal Q=195*.2) Find the component form of the vector that represents the velocity of an airplane descending at a speed of 120 miles per hour at angle of 30* below the horizontal.3) A force of 600 pound is required to pull a boat and trailer up a ramp inclined at 15* from the horizontal . Find the combined weight of the boat and trailer 4) A force of 500 pound is required to pull a boat and trailer up a ramp inclined at 12* from the horizontal . Find the combined weight of the boat and trailer
The minute hand of a wall clock measures 24 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the magnitude and angle from a quarter after the hour to half past, the magnitude and angle for the next half hour, and the magnitude and angle for the hour after that? (Use a coordinate system with the origin at the clock center, +x rightward toward the "3:00" position, and +y upward toward the "12:00" position.) (a) the magnitude from a quarter after the hour to half past cm(b) the angle from a quarter after the hour to half past ° (counterclockwise from the +x-axis)(c) the magnitude for the next half hour cm(d) the angle for the half hour in part (c) ° (counterclockwise from the +x-axis)(e) the magnitude for the hour after that cm(f) What is the angle for the hour in part (e) ° (counterclockwise from the +x-axis)
A particle moves in two dimensional space where i and j are unit vectors in the x and y directions respectively. At time t seconds its displacement from the origin is given by r = (6t - 4t²)i + 2t j where all lengths are measured in metres. (i) Write down the particle's velocity vector in component form. (ii) Find the speed of the particle when t = 2. (iii) Show that the equation of the path of the particle is x = 3y - y².
An ant walks due east at a constant speed of 2 mi/hr on a sheet of paper that rests on a table. Suddenly, the sheet of paper starts moving due southeast at v2 mi/hr. The following is a correct solution for finding the resultant speed and direction of the ant relative to the table. Set up a coordinate system so that the positive y-axis corresponds to north and the positive x-axis corresponds to east. Then the velocity vector for the ant relative to the paper is given by (2,0). The velocity vector for the paper relative to the table is given by (v2 cos (-4), v2 sin (-5))= (1, –1). Therefore, the resultant velocity vector is given by (2,0) + (1, –1) = (3, –1). The speed of the ant relative to the table is v32 + 1² = v10 mi/hr and the direction the ant is traveling relative to the table is found by (금) using tan 0 = -1 where 0 represents the angle made with the positive r-axis. In this case 0 = arctan 3 3
How to solve this question
6. An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of S47°E. Find a vector that represents the resultant velocity of the plane relative to the point of takeoff. Let i point east, j point north, and k point up. (Show work)