Question

ximena 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 = \sqrt{\frac{10000}{m}}. order the equations below to show the steps she would use to solve the equation to find the value of m. \
99^2 = \frac{10000}{m} \
m = \frac{10000}{9801} \
99 = \sqrt{\frac{10000}{m}} \
9801m = 10000

Explanation:

Step1: Start with the given equation

The initial equation is \( 99 = \sqrt{\frac{10000}{m}} \) (since \( 2\times5000 = 10000 \) from kinetic energy formula \( KE=\frac{1}{2}mv^{2}\), so \( 5000=\frac{1}{2}m(99)^{2}\) implies \( 10000 = m(99)^{2}\) and the given equation is \( 99=\sqrt{\frac{10000}{m}}\)).

Step2: Square both sides

To eliminate the square root, square both sides of the equation \( 99 = \sqrt{\frac{10000}{m}} \). Squaring gives \( 99^{2}=\frac{10000}{m} \), and \( 99^{2}=9801 \), so \( 9801=\frac{10000}{m} \).

Step3: Cross - multiply

From \( 9801=\frac{10000}{m} \), cross - multiply to get \( 9801m = 10000 \).

Step4: Solve for m

Divide both sides of the equation \( 9801m = 10000 \) by 9801 to get \( m=\frac{10000}{9801} \).

So the order of the equations is:

1. \( 99=\sqrt{\frac{10000}{m}} \)
2. \( 99^{2}=\frac{10000}{m} \) (i.e., \( 9801=\frac{10000}{m} \))
3. \( 9801m = 10000 \)
4. \( m=\frac{10000}{9801} \)

Answer:

1. \( 99=\sqrt{\frac{10000}{m}} \)
2. \( 99^{2}=\frac{10000}{m} \)
3. \( 9801m = 10000 \)
4. \( m=\frac{10000}{9801} \)