54.
Two forces act an angle of 120degree. If the greater force is 150 N and their resultant ia
perpendicular to the smaller force, the smaller force is
a) 70N
b) 75N
c) 30N
d) 35N
Answers
Answer:
start with the smaller unknown force of BD
ADB = 120 degrees & AD is an = force of BD
BD has a virtual force of BC + CD, C being the midpoint of AB
AD also has a virtual force of AC + CD
AC cancels BC & CD is doubled to CE, hence DE = CD
DF is perpendicular to BD and the bigger force HD that is along the AD line + the smaller BD will end up somewhere on the DF line.
since BD and AD will end up at E, the remainder of the bigger force will venture off of E and will be parallel to AD & HD as no other forces are apposing it. F is where this parallel line crosses the perpendicular DF line. EF will = HA.
ADB =120, AD=BD and C is the midpoint of A&B, both ADC & BDC are 60 degrees each.
because of the 30/60/90 triangle, CD is 1/2 of AD & BD
also ADE & BDE are = & 120 degrees each (360–120)/2
since BDE = 120 & BDF being perpendicular at 90, EDF = 30 degrees
because AD & EF are parallel, and ADE = 120 degrees, DEF also = 120 degrees
triangle DEF has 2 angles 30 & 120 leaving 30 remaining for DFE (180-(120+30))
EDF and DFE both = 30 degrees so triangle DEF is isosceles & thus DE = EF
CD = DE = EF = HA means EF & HA are also 1/2 of AD & BD
smaller force AD + 1/2 AD (HA) = 40
smaller force = 40 / (1+.5) or 40/1.5 or 40/(3/2) or 40*(2/3) or 80/3 or 26 2/3
Answer:
30
I think because it is close to 25