If a ball is thrown downward from the top of a building with initial velocity of 10 m/s and strikes the ground with a speed of 60 m/s , how tall is the building?

Question

This is a differential equations questions I'm working on.

Answer 1

You can work this problem using energy methods.

Let v₁ = velocity at top of building (meters/second)

v₂ = velocity at the ground (meters/second)

h₁ = height of building (meters)

g = gravity acceleration (9.8meters/second2)

Then

mgh₁ + (1/2)mv₁² = (1/2)mv₂² (mass terms cancel and h₂ = 0)

or h₁ = (1/2)(v₂² - v₁²)/g = (1/2)(60²-10²)/(9.8)

h₁ = 178.57 meters