A rocket, initially at rest, is fired vertically with an upward acceleration of 10 m/s^2. At an altitude of 0.50 km, the engine of the rocket cuts off. What is the maximum altitude it achieves?

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Answer 1 · 2016-12-16T04:22:32

1.01 km

You can divide the journey into two stages:

For the 1st stage we can use:

#sf(v^2=u^2+2as)#

#:.##sf(v^2=0+(2xx10xx0.5xx10^3)=10,000)#

#sf(v=sqrt(10,000)=100color(white)(x)"m/s")#

For the 2nd stage this becomes the initial velocity and the acceleration under free fall is equal to minus g.

At the zenith the final velocity will be zero.

So we can write:

#sf(0=100^2-2xx9.8xxh)#

#:.##sf(h=(10,000)/(2xx9.8)=510.2color(white)(x)m)#

The rocket will, therefore, travel a maximum height of 0.5 km plus 510.2 m.

This is equal to 1.01 km.