Final answer:
To find the velocity components of the object after 10.0 seconds, we calculate the net force acting on the object by vector addition of the given forces, use Newton's second law to find the mass, and then apply the kinematic equation for velocity.
Step-by-step explanation:
The question involves finding the velocity components of an object after a certain time, given the forces acting on it and its acceleration. First, we need to find the resultant force by vector addition of the three forces given:
- F1 = (-2.00i + 2.00j) N
- F2 = (5.00i - 3.00j) N
- F3 = (-45.0i) N
Adding these vectors, we get:
Fnet = F1 + F2 + F3 = (-2.00 + 5.00 - 45.0)i + (2.00 - 3.00)j = (-42.0i - 1.00j) N
Given that the object experiences an acceleration of 3.75 m/s2, we can use Newton's second law to find the mass of the object:
Fnet = ma
Solving for mass, m = Fnet / a, we obtain the object's mass. Then, using the kinematic equation v = u + at (where u is the initial velocity, and we will assume it is zero since no initial velocity is given), we can calculate the velocity components after 10.0 seconds. The final velocity components will be the product of the object's acceleration and the time (10.0 s).