Question

kamryn wants to find the mass of an object with 5000 j of kinetic energy and a velocity of 99 m/s. she wrote the equation 99 = √(2(5000)/m). order the equations below to show the steps she would use to solve the equation to find the value of m. 99² = 10000/m, 99 = √(2(5000)/m), m = 10000/9801, 9801m = 10000

Explanation:

Step1: Write the kinetic - energy formula

The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$, where $K$ is kinetic energy, $m$ is mass and $v$ is velocity. Given $K = 5000$ J and $v = 99$ m/s, we can rewrite the formula for $m$ as $m=\frac{2K}{v^{2}}$.

Step2: Substitute the values

Substitute $K = 5000$ and $v = 99$ into the formula: $m=\frac{2\times5000}{99^{2}}$.

Step3: Calculate the denominator

$99^{2}=99\times99 = 9801$.

Step4: Calculate the value of $m$

$m=\frac{10000}{9801}\approx1.02$ kg.

Answer:

The correct order of the equations to solve for $m$ is:

1. Start with the kinetic - energy formula $K=\frac{1}{2}mv^{2}$, and rewrite it as $m = \frac{2K}{v^{2}}$.
2. Substitute $K = 5000$ and $v = 99$ to get $m=\frac{2\times5000}{99^{2}}$.
3. Calculate $99^{2}=9801$.
4. Then $m=\frac{10000}{9801}$.

So the order of the given equations from first to last should be:
$m=\frac{2(5000)}{99^{2}}$, $99^{2}=9801$, $m=\frac{10000}{9801}$, $m\approx1.02$ kg (the last step of actually calculating the numerical value of $m$ which is not in the given list but for completeness). In terms of the given equations in the list, the order is: $m=\frac{2(5000)}{99^{2}}$, $99^{2}=9801$, $m=\frac{10000}{9801}$.