An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= <4 N , 8 N># and the second is #F_2 = < 1 N, 7 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-12-30T07:10:59

The acceleration is #=3.95ms^(-2)# at an angle of #71.6#º

The resultant force is

#vecF=vecF_1+vecF_2#

#vecF_1=〈4,8〉#

#vecF_2=〈1,7〉#

#vecF=〈4,8〉+〈1,7〉=〈5,15〉#

The magnitude of #vecF# is #∥vecF∥=∥〈5,15〉∥#

#=sqrt(5^2+15^2)=sqrt(25+225)=sqrt250=15.8N#

The rate of acceleration is #=F/m=15.8/4=3.95ms^(-2)#

The direction is #=arctan(15/5)=arctan3=71.6#º