I dont need the work to be shown only the answers Please h

Three astronauts, propeled by jet backpacks, push and guide a 130 kg asteroid toward a processing dock, exerting the forces shown in the figure below, with F 1 = 32 N, F 55 N, F3 = 41 N, | = 30°, and 3-60°. (a) What is the asteroid\'s acceleration in unit-vector notation? m/s2 (b) What is the asteroid\'s acceleration as a magnitude and direction? magnitude direction m/s2 o (counterclockwise from the +x axis is positive)

Solution

Problem 1.)

As the forces and the angles are given, we can determine the y and x component of the net force.

Fx = F1 cos 30 + F3 Cos 60 + F2 = 27.7128 + 27.5 + 55 = 110.2128 N

Fy = 32 Sin30 - 41 Sin60 = 16 - 35.507 = -19.507 N

Therefore acceleration would be ax = Fx / m

and ay = Fy /m

That is acceleration in unit vector notation is: 0.8478 i^ - 0.15 j^

Magnitude of acceleration = 0.86097 m/s^2

For direction, we can write tan = 19.507 / 110.2128 = 0.17699

or, = 10.03

Therefore the angle from + x axis in the counterclockwise would be 360 - 10.04 = 349.96 degrees.

Problem 2.) We will balance the force along the direction perpendicular to which Betty is pulling the tire.

Hence, 202 cos47 = 155cos

cos = 0.889

or, = 27.252 degrees.

Now, we balance the forces in direction along which Betty is pulling to get:

F = 202 sin47 + 155sin27.252 = 218.7087 Newtons is the required force with which Betty pulls the tire.

Problem 3.)

As the block is being pulled by an upward force of 1.2 N, the net normal force acting on the block will get reduced.

We can balance the forces acting on the block along the vertical direction to get:

1.2 + N = 3.1

or N = 1.9 N

as the normal force acting on the block is 1.9 N, by newton\'s third law, we can say that the force acting on the surface by the block will be 1.9 N