Ask Question
21 November, 09:44

A falling stone is at a certain instant 90 feet above the ground. Two seconds later it is only 10 feet above the ground. If it was thrown down with an initial speed of 5 feet per second, from what height was it thrown?

+2
Answers (1)
  1. 21 November, 10:28
    0
    the initial height is 90.556 m

    Step-by-step explanation:

    neglecting air friction and the height required to accelerate the rock from 0 to 5 ft/s downwards. Then the only acceleration we are counting is the gravity and from the equations of vertical motion we have:

    h₁=H+vy*t - 1/2*g*t₁²

    h₂=H+vy*t - 1/2*g*t₂²

    subtracting the first equation to the second one

    h₂-h₁ = vy * (t₂-t₁) - 1/2*g * (t₂²-t₁²)

    h₂-h₁ = vy * (t₂-t₁) - 1/2*g * (t₂-t₁) (t₂+t₁)

    denoting Δt = t₂-t₁ and Δh=h₂-h₁

    Δh=vy*Δt-1/2*g*Δt * (t₂+t₁)

    Δh=vy*Δt - 1/2*g*Δt * (2*t₁+Δt)

    1/2*g*Δt * (2*t₁+Δt) = vy*Δt-Δh

    2*t₁+Δt = (vy*Δt-Δh) / (1/2*g*Δt)

    t₁ = (vy*Δt-Δh) / (g*Δt) - Δt/2

    replacing values

    t₁ = (-5ft/s*2 s - (10 ft-90 ft)) / (32.2 ft/s²*2 s) - 2 s/2 = 0.087 s

    then replacing in the first equation

    h₁=H+vy*t - 1/2*g*t₁²

    H = h₁ - vy*t + 1/2*g*t₁²

    H = 90 ft - (-5ft/s) * 0.087 s + 1/2*32.2 ft/s² * (0.087 s) ² = 90.556 m

    then the initial height is 90.556 m
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A falling stone is at a certain instant 90 feet above the ground. Two seconds later it is only 10 feet above the ground. If it was thrown ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers