Hoping for you help and patience (Physics help)

I would like to ask help from you guys, if you could kindly check for any errors that i may have done if any. I HAVE to ace this because this was a recap of what we tackled last quarter. I already aced the examinations yesterday, and if i get this last special homework perfectly, i'll be awarded with some academic merit medal in physics (It's been awhile since i've brought my mother something like that, i'd love to make her happy.)

Answer the following with complete solution, box your final answer.

1. A body of mass 8.0 kg is acted upon by two forces 40 N and 30 N. Find the acceleration of the body if the forces are

a. along the same direction

Ans: 40N+30N=70N 70N = 8.75m/s²
                                     8.0kg
b. in exactly opposite directions

Ans: 40N-30N=10N 10N = 1.25m/s²
                                    8.0kg
c. at right angle to each other.

Ans: √40N²+30N²=50N 50N = 6.25m/s²
                                            8.0kg
2. A force of 3 N acts perpendicularly to a force of 4 N. the resultant force has a magnitude of_________________.

Ans: √3N²+4N²=5N

3. Which force vector is equal to 60 N acting westward?

a. 40 N west b. 60 N northwest c. 60 N eastward d. 60 N westward

Ans: d. 60N Westward

4. Two forces act on point E. one is 20 N north of E, while the other is 20 N, 60 degrees south of E.

a. determine the magnitude and direction of the resultant force.

F1                                                                  F2
X-Component:                                         X-Component:
0N                                                                 Cos60 = o = Cos60(20N)=10N
Y-Component:                                                            20N
20N                                                            Y-Component:
                                                                     Sin60 = a = Sin60(20N)= -17.32N
                                                                                   20n
Ans: √(10N²+2.68²) = 10.35N 15 Degrees north of east.

b. find the magnitude and direction of the equilibrant force.

Ans: 10.35N 15 Degrees south of west.

(#4 A is still being contested on the validity of the question. I already SMSed my teacher. If E is a point, than Force 2 is 60 deg south of nothing? So i assumed the it was also South of East)

mike_mccue


I haven't done vectors in 30 years.

Here's a  bump for the math people to hopefully see.

best regards,
mike

Thank you so much Mike!