Question

an object thrown vertically upward reaches a height of 500m. what was its initial velocity? how long will the object take to come back to the earth?

Answer 1

Given : The distance = s = 500m
             Acceleration due to gravity = g = 10m/s²
             a = -g
               = -10
For the upward motion of the object final velocity = v = 0
To Find : Initial velocity = u = ?
                Time taken by object to come back = 2t = ?
Solution : By Newtons third equation of motion
        v² = u² + 2as
    ∴ 0² = u² + 2(-10 × 500)
    ∴ 0 = u² - 20 × 500
    ∴ 0 = u² - 10000
    ∴ u² = 10000
    ∴ u = √10000
    ∴ u = 100
By Newton's second equation of motion 
    s = ut + 1/2 at²
  ∴ s = 0 × t + 1/2 10 t²
  ∴ 500 = 0 + 5t²
  ∴ 500 = 5t²
  ∴ t² = 500/5
  ∴ t² = 100
 ∴ t = √100
  ∴ t = 10
∴ Total time taken = 2t
                               = 2 × 10
                               = 20s