1. For the displacement vectors d₁(2.44m, 49), d₂(1.68m, 136), and d₃(5.45m, 248), find: d₁+ d₂+ d₃and express in polar (r,q)form.

For this question, enter the following values from your solution (BE SURE TO READ THE NOTES BELOW!):

• x & y components for each displacement vector in blanks 1 to 6 in the following order: (d_1x, d_1y), (d_2x, d_2y), (d_3x, d_3y)
• Sum of d₁+ d₂+ d₃in Cartesian (x, y) form blanks 7 & 8:d_x, d_y(where " " means "the sum of": d_x=d_1x+ d_2x+ d_3x; d_y=d_1y+ d_2y+ d_3y)
• (d_x, d_y) in Polar form blanks 9 & 10: (r,q)

NOTE:

• Enter all ANSWERS TO 2 DECIMAL VALUES ONLY (e.g. round an answer of "0.304" to enter as "0.30"; entering "0.3", ".3", ".30" would all be incorrect)
• BUT - carry at least one extra decimal value when using intermediate values to calculate subsequent values. For example:
• Answer for d1x entered to 2 decimal values (e.g. "-2.15 m" entered from calculated answer of "-2.154")
• BUTuse >2 decimal values for d1x when summing with d2x & d3x (e.g. d_x=d1x + d2x + d3x = -2.154 m - 1.828 m + 3.602 m)
• INDICATE IF ANSWER IS NEGATIVE by including a "-" sign (e.g. -4.06 m)
• INCLUDE UNITS for x, y, and r values (e.g. enter answer of "3.891" for d3y as "3.89 m")
• Angle values:must be in degrees BUT angle unit/symbol NOT required

2.Consider the following system of forces and accompanying equations:

• F₁is an unknown force that balances with forces F₂and F₃(i.e. all forces sum to zero, as shown in the equations)
• The angle of the F₂force vector is given, 225, but magnitude is unknown
• F₃is a force acting at -55 with a magnitude of 350 N.

Solve for the unknown forces F₁and F₂in polar form, given the following system of equations:

F_1x+ F_2x+ F_3x= 0

F_1y+ F_2y+ F_3y= 0

F₃*d₃- (F₂*d₂) = 0

where d₂= 0.07 m, d₃= 0.15 m

Consider sketching out the vectors to assist your answer

NOTE:

Enter your calculated values for the listed intermediate variables as well as final values for the missing polar coordinates:

• x & y components for each force: F_1x, F_1y, F_2x, F_2y, F_3x, F_3y(determining these are a hint btw!)
• Missing r & values: F₁,q_F1, F₂, where F₁& F₂are the polar magnitudes (r) andq_F1is the polar angle for F₁

Entering values/answers:

• Enter all answers to 2 decimal values (e.g. "105.20"; "105.2" would be incorrect)
• Indicate if values are negative (e.g. "-105.20")
• Include units for the x & y components as well as r (e.g. "162.36 N")
• Enterq_F1in degrees as a positive (CCW) value, do NOT include degree unit in answer (e.g. "79.91")