A planet orbits a star in an elliptical orbit. At a particular instant the momentum of the planet is <-3.3 x 1029, -1.6 x 1029, 0> kg-m/s, and the force on the planet by t -star is <-2.3 × 10²², -1 × 1023, 0> N. Find F₁ and FL. (Express your answers in vector form.) 7₁=3 F₁ = 7 the tolerance is +/-5% 0 N > N

Vectors A and B are two orthogonal vectors in the xy -plane and they have identical magnitudes. If A=3.0 i+4.0 j , find B .

The velocity of a 10-kg object is given by v=5t2i(7t+2t3)j, where if t is in seconds, then v will be in meters per second. a. What is the net force on the object as a function of time? b. What is the momentum of the object when t = 15.0 s?

Two planets in circular orbits around a star have speed of v and 2v . (a) What is the ratio of the orbital radii of the planets? (b) What is the ratio of their periods?

A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69

At one point in space, the direction of the electric field vector Is given In the Cartesian system by the unit vector . If the magnitude of the electric field vector is E=400.0V/m , what are the scalar components , and of the electric field vector at this point? What is the direction angle of the electric field vector at this point?

between points in a plane do not change when a coordinate system is rotated In other words, the magnitude of a vector Is invariant under rotations of the coordinate system. Suppose a coordinate system S is rotated about its origin by angle to become a new coordinate system S’, as shown in the following figure. A point in a plane has coordinates (x,y)in S and coordinates (x,y) in S’. (a) Show that, during the transformation of rotation, the coordinates in S are expressed in terms of the coordinates in S by the following relations: {x=xcos+ysiny=xsin+ycos (b) Show that the distance of point Pto the origin is invariant under rotations of the coordinate system. Here, you have to show that x2+y2=x2+y2. (c) Show that the distance between points Pand Q is invariant under rotations of the coordinate system. Here, you have to show that ( xP =xQ )2+( yP yQ )2=( xP =xQ )2+( yP yQ )2 .

A girl, moving at 8 m/s on in-line skates, is overtaking a boy moving at 5 m/s as they both skate on a straight path. The boy losses a ball backward toward the girl, giving it speed 12 m/s relative to him. What is the speed of the ball relative to the girl, who catches it? (a) (8 + 5 + 12) m/s (b) (8 - 5 - 12) m/s (c) (8 + 5 - 12) m/s (d) (8 5 + 12) m/s (e) (8 + 5 + 12) m/s

Find the angles that vector makes with the and axes.

The polar coordinates of a point are 4/3and 5.50 m. What are its Cartesian coordinates?