while a dog runs forward, its owner pulls back with a 22.4 n force at a 115° direction, doing -42.3 j of…

while a dog runs forward, its owner pulls back with a 22.4 n force at a 115° direction, doing -42.3 j of work. how far did the dog move? (unit = m)

while a dog runs forward, its owner pulls back with a 22.4 n force at a 115° direction, doing -42.3 j of work. how far did the dog move? (unit = m)

Answer

Explanation:

Step1: Recall work - formula

The work formula is $W = Fd\cos\theta$, where $W$ is work, $F$ is force, $d$ is displacement, and $\theta$ is the angle between the force and the displacement. We need to solve for $d$.

Step2: Rearrange the formula for $d$

$d=\frac{W}{F\cos\theta}$.

Step3: Substitute the given values

Given $W=- 42.3\ J$, $F = 22.4\ N$, and $\theta = 115^{\circ}$. First, find $\cos(115^{\circ})\approx - 0.4226$. Then $d=\frac{-42.3}{22.4\times(-0.4226)}$.

Step4: Calculate the value of $d$

$d=\frac{-42.3}{-9.46624}\approx4.47\ m$.

Answer:

$4.47$