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
:

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Answer:
0.69
Explanation:
Sum of the forces on the sled in the y direction:
∑F = ma
Fn - 52 N = 0
Fn = 52 N
Sum of the forces on the sled in the x direction:
∑F = ma
36 N - Fn μ = 0
Fn μ = 36 N
μ = 36 N / Fn
Substitute:
μ = 36 N / 52 N
μ = 0.69