A mass, as shown initially resting against a support, after force $F$ acts on the mass for a $3$ seconds. The time profile of the force is shown in the figure. The impulse momentum principle equation used to solve for $V2$ is given by

Select one:

a$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{500}{3})dt-3$mgsin$-3{}_k$mgcos$=mv2-mv1$

b$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(1500)dt-3$mgsin$-3{}_k$mgcos$=mv2-mv1$

c$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(1500)dt-3$mgsin$-3n_k$mgcos$=mv2-mv1$

d$.$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{500}{3})dt+3$mgsin$-3{}_k$mgcos$=mv2-mv1$