Answer: b. Throw it directly away from the space station.
Explanation:
According to <u>Newton's third law of motion</u>, <em>when two bodies interact between them, appear equal forces and opposite senses in each of them.</em>
To understand it better:
Each time a body or object exerts a force on a second body or object, it (the second body) will exert a force of equal magnitude but in the opposite direction on the first.
So, if the astronaut throws the wrench away from the space station (in the opposite direction of the space station), according to Newton's third law, she will be automatically moving towards the station and be safe.
it is just a matter of integration and using initial conditions since in general dv/dt = a it implies v = integral a dt
v(t)_x = integral a_{x}(t) dt = alpha t^3/3 + c the integration constant c can be found out since we know v(t)_x at t =0 is v_{0x} so substitute this in the equation to get v(t)_x = alpha t^3 / 3 + v_{0x}
similarly v(t)_y = integral a_{y}(t) dt = integral beta - gamma t dt = beta t - gamma t^2 / 2 + c this constant c use at t = 0 v(t)_y = v_{0y} v(t)_y = beta t - gamma t^2 / 2 + v_{0y}
so the velocity vector as a function of time vec{v}(t) in terms of components as[ alpha t^3 / 3 + v_{0x} , beta t - gamma t^2 / 2 + v_{0y} ]
similarly you should integrate to find position vector since dr/dt = v r = integral of v dt
r(t)_x = alpha t^4 / 12 + + v_{0x}t + c let us assume the initial position vector is at origin so x and y initial position vector is zero and hence c = 0 in both cases
r(t)_y = beta t^2/2 - gamma t^3/6 + v_{0y} t + c here c = 0 since it is at 0 when t = 0 we assume
r(t)_vec = [ r(t)_x , r(t)_y ] = [ alpha t^4 / 12 + + v_{0x}t , beta t^2/2 - gamma t^3/6 + v_{0y} t ]
Answer:
B - A
Explanation:
For the combination of 2 vector to due southwest, 1 vector must due south and the other vector due west. Since vector B is already due west, vector A should due south. As vector A is already due north, vector -A would due south. So the combination of B + (-A) or B - A should points southwest
Answer:
See the explanation below.
Explanation:
This analysis can be easily deduced by means of Newton's second law which tells us that the sum of the forces or the total force on a body is equal to the product of mass by acceleration.
∑F = m*a
where:
F = total force [N]
m = mass [kg]
a = acceleration [m/s²]
We must clear the acceleration value.
We see that the term of the mass is in the denominator, so that if the value of the mass is increased the acceleration decreases, since they are inversely proportional.
Explanation:
It is given that,
Mass of the box, m = 100 kg
Left rope makes an angle of 20 degrees with the vertical, and the right rope makes an angle of 40 degrees.
From the attached figure, the x and y component of forces is given by :
Let 
and 
is the resultant in x and y direction.
As the system is balanced the net force acting on it is 0. So,
.............(1)
..................(2)
On solving equation (1) and (2) we get:
(tension on the left rope)
(tension on the right rope)
So, the tension on the right rope is 1063.36 N. Hence, this is the required solution.
