Attempt in Progress Three astronauts, propelled by jet backpacks, push and guide a 100 kg asteroid toward a processing dock, exerting the forces shown in the figure, with F₁ = 27 N, F₂ = 55 N, F3 = 39 N, 0₁ = 30°, and 03 = 60°. What is the (a) magnitude and (b) angle (measured relative to the positive direction of the x axis in the range of (-180°, 180°]) of the asteroid's acceleration? (a) Number (b) Number i Units Units

What is the direction of the vector r= -6.7i - 5.0j? where i and j represent the x-and y- unit vectors?

The magnitude F (in newtons) of a force F and the magnitude G (in newtons) of a force G satisfy the vector equation 2Fi-3Fj+2Gi+2Gj-3i=0 where i and j are the Cartesian unit vectors. What is the value of F? 9 10 3 O 5/60/5 10 06

The figure shows four vectors, A, B, C, and D, having magnitudes 8.0 m, 15.0 m, 12.0 m, and 4.0 m, respectively. The sum of these four vectors is 30° y B 30° X

A soccer ball is kicked with a speed of 9.0 m/s at an angle of 25° above the horizontal. Write the ball's velocity in terms of rectangular unit vectors, using the standard notation that î is horizontal and ĵ is vertical.

Consider the two vectors A-5i-j and B = - i- 4j. (a) Calculate A+B i+ (b) Calculate A -R i (c) Calculate A+ E (d) Calculate A - E (e) Calculate the directions of A +B and A-B. * (counterclockwise from the +x axis) A - B * (counterclockwise from the +x axis)

In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: 2.50 km 45.0° north of west; then 4.20 km 60.0° south of east; then 1.50 km 25.0° south of west; then 5.30 km straight east; then 1.90 km 5.00° east of north; then 7.20 km 55.0° south of west; and finally 2.90 km 10.0° north of east. What is his final position relative to the island? (i.e., find the magnitude and direction of the displacement.) km at degrees South of East

Two forces F1 and F2 act at point O. R is the resultant of force F1 and F2, and it is expressed as R = F1 + F2. Given the magnitude of |F1| = 60 N and |R| = 100 N, calculate. must use parallelogram law/triangle rule and sine & cosine laws.

F5+F6+F7= -0.117i + 0.059j   what would be the polar coordinates of this vector.

The velocity vector of a sprinting cheetah has x- and y-components vx = +28.6 m/s and vy = −26.3 m/s. What angle does the velocity vector make with the +x-axis?