A 300-kg boat is sailing 17.0° north of east at a speed of 1.60 m/s. 35.0 s later, it is sailing 37.0° north of east at a speed of 4.00 m/s. During this time, three forces act on the boat: a 32.2-N force directed 17.0° north of east (due to an auxiliary engine), a 24.1-N force directed 17.0° south of west (resistance due to the water), and F (due to the wind). Find the (a) the magnitude and (b) direction of the force F. Express the direction as an angle with respect to due east.

Three astronauts, propelled by jet backpacks, push and guide a 129 kg asteroid toward a processing dock, exerting the forces shown in the figure, with F₁ = 35.0 N, F₂ = 53.0 N, F3 = 40.0 N, 0₁ = 30.0°, and 03 = 60.0°. 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 Units Units F3 F₂ X

Four forces act on an object, given by F1= 40 N east, F2= 50 N north, F3=70 N west, and F4= 90 N south. What is the magnitude of the net force on the object? O (a) 50 N O (b) 70 N O (c) 131 N O (d) 170 N (e) 250 N

The forces F1, F2, F3, ..... , Fn acting on an object are in equilibrium if the resultant force is the zero vector: F1 + F2 + F3 + g + ........+ Fn = 0. The given forces F1 = 3i - 5j, F2 = 6i + 2j are acting on an object. Then, a. Find the resultant force. b What additional force is required for the given forces to be in equilibrium?

A constant horizontal force pushes a 7.50 kg FedEx package across a frictionless floor on which an xy coordinate system has been drawn. The figure gives the package's x and y velocity components versus time t. What are the (a) magnitude and (b) direction of F? Give the direction as a positive or negative angle of magnitude less than 180° relative to the +x-axis. Vy (m/s) v (m/s) x 10 5 (a) Number (b) Number 1 a 2 Units Units t (s) 3 0 -5 -10 IL 0 ◄► 3 t(s)

An antelope is being pulled by two forces whose vector-component expressions are: F1 = -3.5Ni + 3.4Nj + 3.9Nk F2 = 3Ni + 2.6Nj + -1.5Nk What is the angle (in degrees) between these two vectors?

Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead of the donkey with a force of 81.9 N, Jill pulls with 69.1 N in a direction 45° to the left, and Jane pulls in a direction 45° to the right with 175 N. (Since the donkey is involved with such uncoordinated people, who can blame it for being stubborn?) Find the magnitude of the net force the people exert on the donkey.

Two blocks A and B with mA = 1.1 kg and mB = 0.88 kg are connected by a string of negligible mass. They rest on a frictionless horizontal surface. You pull on block A with a horizontal force of 6.7 N.

Blocks with masses of 1.2 kg, 2.4 kg, and 3.0 kg are lined up in a row on a frictionless table. All three are pushed forward by a 14 N force applied to the 1.2 kg block. How much force does the 2.4 kg block exert on (a) the 3.0 kg block and (b) the 1.2 kg block?

A skier is pulled up a slope at a constant velocity by a tow bar. The slope is inclined at 25.0° with respect to the horizontal. The force applied to the skier by the tow bar is parallel to the slope. The skier's mass is 55.0 kg , and the coefficient of kinetic friction between the skis and the snow is 0.120. Find the magnitude of the force that the tow bar exerts on the skier.