A particle is in uniform circular motion about the origin of an xy coordinate system, moving clockwise with a period of 8.80 s. At one instant, its position vector (from the origin) is 7 = (2.90 m )i – (4.10 m )j. At that instant, what is its velocity in unit-vector notation?

At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 8.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 55.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball?  yards (b) What if? The receiver that catches the football travels 64.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?

A straight river flows east at a speed of 9 mi/h. A boater starts at the south shore of the river and heads in a direction 60° from the shore (see the figure). The motorboat has a speed of 18 mi/h relative to the water. (Assume that the i vector points east, and the j vector points north.) N 60° (a) Express the velocity of the river as a vector in component form. (b) Express the velocity of the motorboat relative to the water as a vector in component form. (Round your answer to two decimal places.) (c) Find the true velocity of the motorboat. (Round your answer to two decimal places.) (d) Find the true speed of the motorboat. (Round your answer to one decimal place.) mi/h Find the direction of the motorboat. (Round your answer to one decimal place.) N ° E

The position r of a particle moving in an xy plane is given by ř seconds. In unit-vector notation, calculate (a) 7, (b) V , and (c) a for t = 3.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 3.00 s? Give your answer in the range of (-180°; 180°). (4.00r3 – 1.00t)î + (5.00 – 1.00r4)j with 7 in meters and t in (a) Number i i Units (b) Number ît i Units i (c) Number i i Units (d) Number i Units

A bird flies 10 m at an angle of 45°. Then it flies 20 m at an angle of 135°. What are the x and y components of the bird's displacement vector at the end of the two flights? Group of answer choices (x,y) = (15 √ 2 ,−5 √ 2)m (x,y) = (−15 √ 2 ,5 √ 2)m (x,y) = (5 √ 2 , 15 √ 2) m (x,y) = (−5 √ 2 ,15 √ 2)m (x,y) = (5 √ 2 ,−15 √ 2)m

A turtle ambles leisurely from a location with position vector r1,x = 1.87 m and ri.y = -2.95 m in a lettuce garden to another location with position vector r2.x = 3.91 m and r2.y = -4.27 m, where the lettuce appears to be tastier. The excursion takes 5.17 min to complete. What are the components and the magnitude of the turtle's average velocity in meters per second? Vav,x m/s Vav,y m/s %3D m/s %3D

At what initial speed must the basketball player in the figure throw the ball, at angle 0 = 40° above the horizontal, to make the foul shot? The horizontal distances are d₁ = 0.9 ft and d2 = 13 ft, and the heights are h₁ = 6.4 ft and h₂ = 10 ft. % hq