Answer:
Distance, d = 0.1 m
It is given that,
Initial velocity of meson,
Finally, the meson is coming to rest v = 0
Acceleration of the meson, (opposite to initial velocity)
Using third equation of motion as :
s is the distance the meson travelled before coming to rest.
So,
s = 0.1 m
The meson will cover the distance of 0.1 m before coming to rest. Hence, this is the required solution.
Before the engines fail
, the rocket's horizontal and vertical position in the air are


and its velocity vector has components


After
, its position is


and the rocket's velocity vector has horizontal and vertical components


After the engine failure
, the rocket is in freefall and its position is given by


and its velocity vector's components are


where we take
.
a. The maximum altitude occurs at the point during which
:

At this point, the rocket has an altitude of

b. The rocket will eventually fall to the ground at some point after its engines fail. We solve
for
, then add 3 seconds to this time:

So the rocket stays in the air for a total of
.
c. After the engine failure, the rocket traveled for about 34.6 seconds, so we evalute
for this time
:
