Question

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)

Answer 1

1000 m/s ( 990.45 m/s to be exact)

Step-by-step explanation:

If we use one of the SUVAT equations, i.e.,

2as = (v^2) - (u^2) where;

s = distance, a = acceleration, v = final velocity, u = initial velocity

At max point the rocks are considered stationery, which makes v = 0, the height is 50,000m which makes s = 50,000, the acceleration is -9.81, as the object decelrates to 0

2(-9.81)(50000) = (0)^2 - (u)^2

-981000 = - u^2

u = sqr root( 981000)

u = 990.45 m/s = 1000 m/s

Answer 2

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=√(v^2+2ah) \\\\v_0 =√( 0+2(10\;m/s^2)(50000\;m))\\\\v_0 =√( 2(10\;m/s^2)(50000\;m)) \\\\v_0 = 1000\;m/s`