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.

A ship is sailing at a speed of 14 mi/hr in the direction S50°E. Express its velocity v as a vector.

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

If v = 3i - 4j is a velocity vector, express v as a product of its magnitude (its speed) times its direction.

A velocity vector of variable magnitude of an object can have a constant direction. O True O False