# 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?

Dec 30, 2016

The acceleration is $= 3.95 m {s}^{- 2}$ at an angle of $71.6$º

#### Explanation:

The resultant force is

$\vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2}$

vecF_1=〈4,8〉

vecF_2=〈1,7〉

vecF=〈4,8〉+〈1,7〉=〈5,15〉

The magnitude of $\vec{F}$ is ∥vecF∥=∥〈5,15〉∥

$= \sqrt{{5}^{2} + {15}^{2}} = \sqrt{25 + 225} = \sqrt{250} = 15.8 N$

The rate of acceleration is $= \frac{F}{m} = \frac{15.8}{4} = 3.95 m {s}^{- 2}$

The direction is $= \arctan \left(\frac{15}{5}\right) = \arctan 3 = 71.6$º