Free Fall Physics Example 2

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Example 2

medium
A ball is thrown upward with an initial velocity of 20 m/s20 \text{ m/s}. How high does it go, and how long until it returns? Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Solution

  1. 1
    At maximum height, v=0v = 0. Use v2=v02−2ghv^2 = v_0^2 - 2gh: 0=202−2(9.8)h  ⟹  h=40019.6≈20.4 m0 = 20^2 - 2(9.8)h \implies h = \frac{400}{19.6} \approx 20.4 \text{ m}
  2. 2
    Time to reach max height: tup=v0g=209.8≈2.04 st_{\text{up}} = \frac{v_0}{g} = \frac{20}{9.8} \approx 2.04 \text{ s}.
  3. 3
    Total time (up and down, symmetric): ttotal=2×2.04≈4.08 st_{\text{total}} = 2 \times 2.04 \approx 4.08 \text{ s}

Answer

hmax⁡≈20.4 m,ttotal≈4.08 sh_{\max} \approx 20.4 \text{ m}, \quad t_{\text{total}} \approx 4.08 \text{ s}
A ball thrown upward decelerates due to gravity, momentarily stops at maximum height, then accelerates downward. The motion is symmetric: time up equals time down.

About Free Fall

Motion under gravity alone, with no air resistance — all objects in free fall accelerate at g≈9.81g \approx 9.81 m/s² regardless of mass.

Learn more about Free Fall →

More Free Fall Examples

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A stone is dropped from a cliff. How far does it fall in [formula]? Use [formula].

Example 3 easy

An object is dropped from a height of [formula]. How long does it take to hit the ground? Use [formu

Example 4 medium

A ball is thrown straight up with an initial velocity of [formula]. Using [formula]: (a) How long un

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