Physics question

Question

You are an astronaut visiting Titan, a moon of Saturn, and throw a rock vertically upwards. The rock leaves your hand at 7.50 m/s, and after the rock has risen 7 m, you measure it to have an upwards velocity of 6.09 m/s. (a) What is the acceleration on Titan? (b) What is the maximum height that the rock reaches?

Answer 1

(a)

 

Use the kinematic relation

 

v₂² - v₁² = 2ad ⇒

 

a = (v₂² - v₁²) / (2d)

 

Plug in these values and get a in m/s²:

 

v₂ = 6.09 m/s

v₁ = 7.50 m/s

d = 7 m

 

The minus sign in the result just means the acceleration is opposite the upward motion of the rock.

 

(b)

 

Get maximum height from energy conservation.  Set kinetic energy at the bottom equal to gravitational potential energy at the top.

 

v₁²/2 = |a|h_max

 

h_max = v₁² / (2|a|)

 

Plug in v₁ and |a| from part (a) and get h_max in meters.  You should be able to finish from here.