Physics: When some volcanoes erupt, big rocks have been measured to reach heights of 50km (50,000m) What would the initial velocity need to be in order to reach such heights (neglect air resistance) (1 sigfig space unit)

When some volcanoes erupt, big rocks have been measured

ninaaforever

12.02.2022

We know that:

v² = v₀² - 2ah

Where v is the final velocity whos value at the maximum height is zero.

v₀ is the initial velocity

h is the maximum height

a = g = 10 m/s² the acceleration due gravity on Earth

Solving for v0:

$v_0=\sqrt{v^2+2ah} \\\\v_0 =\sqrt{ 0+2(10\;m/s^2)(50000\;m)}\\\\v_0 =\sqrt{ 2(10\;m/s^2)(50000\;m)} \\\\v_0 = 1000\;m/s$

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