Question

The ratio of the final kinetic energy to the initial kinetic energy of an object is one half. If the initial velocity of the object is 10m/s, what is the final velocity?Select one:О A. 2.7 m/sO B 1.5 m/sO C. 7.1 m/sO D. 10 m/sO E. 20 m/s

Answer 1

The final velocity of the object is approximately 7.1 m/s, as calculated by applying the kinetic energy formula and solving for the final velocity given that the final kinetic energy is half of the initial.

Step-by-step explanation:

The kinetic energy (KE) of an object is given by the equation KE = 0.5 × m × v^2, where m is the mass of the object and v is its velocity. If the final kinetic energy is half of the initial kinetic energy, the equation can be setup as follows: 0.5 × m × v_final^2 = 0.5 × (1/2) × m × v_initial^2. Cancelling out the common factors and substituting the given initial velocity of 10 m/s, we have v_final^2 = (1/2) × (10 m/s)^2. Therefore, v_final = √((1/2) × 10^2) = √50, which is approximately 7.1 m/s.

Answer 2

Given data:

* The initial velocity of the object is 10m/s.

* The ratio of the final kinetic energy to the initial kinetic energy is half.

Soluiton:

The kinetic energy in terms of mass and velocity of the object is,

`\begin{gathered} (K_f)/(K_i)=((1)/(2)mv^2)/((1)/(2)mu^2) \\ (K_f)/(K_i)=(v^2)/(u^2) \end{gathered}`

where v is the final velocity and u is the initial velocity, K_f is the final kinetic energy, and K_i is the initial kinetic energy,

Substituting the known values,

`\begin{gathered} (1)/(2)=(v^2)/(10^2) \\ v^2=(100)/(2) \\ v^2=50 \\ v=7.07\text{ m/s} \\ v\approx7.1\text{ m/s} \end{gathered}`

Thus, the final velocity of the object is 7.1 m/s.

Hence, option C is the correct answer.