Answer:
- The magnitude of the vector
is 107.76 m
Explanation:
To find the components of the vectors we can use:

where
is the magnitude of the vector, and θ is the angle over the positive x axis.
The negative x axis is displaced 180 ° over the positive x axis, so, we can take:






Now, we can perform vector addition. Taking two vectors, the vector addition is performed:

So, for our vectors:


To find the magnitude of this vector, we can use the Pythagorean Theorem



And this is the magnitude we are looking for.
The change in velocity is 5m/s which added to the initial 3m/s makes the final velocity 8m/s
Distance = (3*5) + (1/2*1*5^2)= 15+12.5= 27.5m
At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:

while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:

And the total energy of the system is

Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:

while the mass is moving at speed v, and therefore the kinetic energy is

And the total energy is

For the law of conservation of energy, the total energy must be conserved, therefore

. So we can write

that we can solve to find an expression for v:
Is there a multiple choice?
Answer:
c) 11.9 yr
Explanation:
The orbital period is proportional to r^(3/2) and does not depend on the satellite's mass. Any object at Jupiter position will have the same orbital period regardless of mass.
By keppler's law we know that
T^2= r^3
T= orbital time period
r= mean distance of the planet from the Sun.
clearly, The orbital period does not depend on the satellite's mass
there, the correct answer will be c= 11.9 yr.