Question

A 2 kg rocket is launched straight up into the air with a speed that allows it to reach a height of 100 meters, even though air resistance performs 800 J of work on the rocket. Determine the launch speed of the rocket. How high would the rocket travel if air resistance is ignored?

Answer 1

v = 52.5 m/s and h = 140.6 m

Step-by-step explanation:

We use the energy work relationship

W = ΔEm

W = - 800 J

The negative sign is because rubbing always opposes movement

Let's write it enegia in two points

Lower initial

Em₀ = K = ½ m v²

Highest final

`Em_(f)` = U = mg h

W =
`Em_(f)` - Emo

800 = ½ m v² - m g h

v² = (800+ m gh) 2 / m

v = √ (800 + 2 9.8 100) 2/2

v = 52.5 ms

we ignoring the existence of air the height is

`Em_(f)` = Em₀

½ m v² = m g h

h = v² / 2g

h = 52.5²/2 9.8

h = 140.6 m