A rocket is fired vertically up from the ground with an acceleration of 10m/{{s}^{2}}. If its fuel is finished after 1 minute then calculate-(a) Maximum velocity attained by rocket in ascending motion. (b) Height attained by rocket before fuel is finished.(c) Time taken by the rocket in the whole motion.(d) Maximum height attained by rocket.

To solve this problem, we'll use the equations of motion for uniformly accelerated motion.

(a) Maximum velocity attained by the rocket in ascending motion:
We know that the rocket's acceleration is 10 m/s^2. We can use the equation:

v = u + at

where:
v = final velocity
u = initial velocity (which is 0 since the rocket starts from rest)
a = acceleration
t = time

In this case, we're interested in the maximum velocity, so we need to find the time when the rocket runs out of fuel. Given that the fuel is finished after 1 minute, we convert this to seconds: t = 60 seconds.

Substituting the values into the equation, we have:

v = 0 + (10 m/s^2) * (60 s) = 600 m/s

Therefore, the maximum velocity attained by the rocket in ascending motion is 600 m/s.

(b) Height attained by the rocket before fuel is finished:
To find the height attained, we can use the equation:

s = ut + (1/2)at^2

where:
s = distance or height
u = initial velocity (0 m/s)
t = time
a = acceleration (10 m/s^2)

Substituting the values, we have:

s = 0 + (1/2) * (10 m/s^2) * (60 s)^2 = 18,000 m

Therefore, the height attained by the rocket before the fuel is finished is 18,000 meters.

(c) Time taken by the rocket in the whole motion:
The rocket's motion consists of two parts: ascending with acceleration and descending with deceleration due to gravity. Since the rocket starts and ends at rest, the time taken in each phase is the same.

To find the total time, we need to consider both the ascending and descending motion. The ascending motion time can be found using the equation:

v = u + at

where:
v = final velocity (0 m/s at the top)
u = initial velocity (0 m/s)
a = acceleration (10 m/s^2)
t = time

Since the rocket starts from rest and reaches a maximum velocity of 600 m/s, the time taken in ascending motion is:

0 + (10 m/s^2) * t = 600 m/s
10t = 600
t = 60 s

The descending motion also takes 60 seconds, so the total time taken by the rocket in the whole motion is 60 + 60 = 120 seconds.

(d) Maximum height attained by the rocket:
The maximum height can be found using the equation:

s = ut + (1/2)at^2

We can use half of the total time (60 seconds) to find the maximum height during the ascending motion:

s = 0 + (1/2) * (10 m/s^2) * (60 s/2)^2 = 9,000 m

Therefore, the maximum height attained by the rocket is 9,000 meters.