A 0.5 kg bird starts off flying at a height of 30 m. At this height, the system has 20 J of gravitational potential energy. If the system has a final gravitational energy of 30 J, what is the final height of the bird?

45 m

Explanation:

From the question given above, the following data were obtained:

Mass (m) = 0.5 kg

Initial height (h₁) = 30 m

Initial potential energy (PE₁) = 20 J

Final potential energy (PE₂) = 30 J

Final height (h₂) =?

From:

PE = mgh

PE / h = mg = constant

Thus,

PE₁ / h₁ = PE₂ / h₂

With the above formula, we can obtain the final height of the bird as follow:

Initial height (h₁) = 30 m

Initial potential energy (PE₁) = 20 J

Final potential energy (PE₂) = 30 J

Final height (h₂) =?

PE₁ / h₁ = PE₂ / h₂

20 / 30 = 30 / h₂

Cross multiply

20 × h₂ = 30 × 30

20 × h₂ = 900

Divide both side by 20

h₂ = 900 / 20

h₂ = 45 m

Therefore, the final height of the bird is 45 m.

Explanation:

It is given that,

Mass of moon,

Radius of circle,

The time required for one revolution is 27.3 days, t = 27.3 days

1 day = 86400 seconds

27.3 days = 2358720 seconds

Let v is the speed of moon around the circular path. It is given by :

v = 1017.57 m/s

Let F is the centripetal force acting on the moon. It is given by :

So, the centripetal force that must act on the moon is . The gravitational force that the earth exerts on the moon at that same distance is also equal to . Hence, this is the required solution.