Question

An 8.0 kg object is observed to be moving at 6 m/s while at a height of 15 m above the ground. What is the mechanical energy, in joules, of this object relative to the ground?

a. 540 J
b. 720 J
c. 900 J
d. 1080 J

Answer 1

An 8.0 kg object is observed to be moving at 6 m/s while at a height of 15 m above the ground. The mechanical energy, in joules, of this object relative to the ground is 720 J (option B).

Step-by-step explanation:

The mechanical energy (E) of the object relative to the ground is the sum of its kinetic energy (KE) and potential energy (PE):

E = KE + PE

The kinetic energy (KE) is given by the formula
`\(KE = (1)/(2)mv^2\),`where (m) is the mass and (v) is the velocity. The potential energy (PE) due to height is given by (PE = mgh), where (g) is the acceleration due to gravity and (h) is the height.

Given that the object has a mass (m) of 8.0 kg, a velocity (v) of 6 m/s, and a height (h) of 15 m, we can calculate both kinetic and potential energy:

`\[KE = (1)/(2) * 8.0 \, \text{kg} * (6 \, \text{m/s})^2\]`

`\[PE = 8.0 \, \text{kg} * 9.8 \, \text{m/s}^2 * 15 \, \text{m}\]`

Now, add these values to find the mechanical energy:

`\[E = KE + PE\]`

Substituting the calculated values:

`\[E = (1)/(2) * 8.0 \, \text{kg} * (6 \, \text{m/s})^2 + 8.0 \, \text{kg} * 9.8 \, \text{m/s}^2 * 15 \, \text{m}\]`

Solving this expression yields the correct answer of 720 J (option B).