3. If the only forces acting on a 2.0 -kg mass are overrightarrow (F)_(1)=(3hat (i)-8hat (j))N and overrightarrow (F)_(2)=(5hat (i)+3hat (j))N , what is the acceleration of the mass?

To find the acceleration of the mass, we need to calculate the net force acting on it and then divide it by the mass.<br /><br />Given:<br />Force 1: $\overrightarrow {F}_{1}=(3\hat {i}-8\hat {j})N$<br />Force 2: $\overrightarrow {F}_{2}=(5\hat {i}+3\hat {j})N$<br />Mass: $m.0\,kg$<br /><br />Step 1: Calculate the net force.<br />$\overrightarrow {F}_{net}=\overrightarrow {F}_{1}+\overrightarrow {F}_{2}$<br />$\overrightarrow {F}_{net}=(3\hat {i}-8\hat {j})+(5\hat {i}+3\hat {j})$<br />$\overrightarrow {F}_{net}=(3+5)\hat {i}+(-8+3)\hat {j}$<br />$\overrightarrow {F}_{net}=8\hat {i}-5\hat {j}$<br /><br />Step 2: Calculate the acceleration.<br />$a=\frac {\overrightarrow {F}_{net}}{m}$<br />$a=\frac {8\hat {i}-5\hat {j}}{2.0\,kg}$<br />$a=4\hat {i}-2.5\hat {j}\,m/s^2$<br /><br />Therefore, the acceleration of the mass is $4\hat {i}-2.5\hat {j}\,m/s^2$.