A stationary rocket is launched vertically upward. After 4s, the rocket's fuel is used up and it is 225.6 m above the ground. At this instant the velocity of the rocket is 112,8 m/s. Then the rocket undergoes free fall. Ignore the effect of the air friction.Assume that g does nt change the entire motion of the rocket. Taking up as positive,use equation of motion to determine the time taken from the moment the rocket is launched until it strikesthe ground.

Tr = To + (-Vo)/g = 4 + (-112.8)/-9.8 =

15.51 s. = Rise time.

hmax = ho + (V^2-Vo^2)/2g
hmax = 225.6 + (0-(112.8)^2)/-19.6 =
1506 m. Above gnd.

hmax = 0.5g*t^2 = 1506 m.
4.9t^2 = 1506
t^2 = 307.3
Tf = 17.53 s. = Fall time.

T = Tr + Tf = 15.51 + 17.53 = 33.0 s. =
Time in air.

To determine the time taken from the moment the rocket is launched until it strikes the ground, we will break down the motion of the rocket into two parts: the upward motion until fuel is used up, and the subsequent downward motion during free fall.

First, let's calculate the initial velocity of the rocket when it is launched. Since the rocket starts from rest, the initial velocity is 0 m/s.

Using the equation of motion:
v = u + at

where
v = final velocity
u = initial velocity
a = acceleration
t = time

We can rearrange the equation to solve for the time taken for the rocket to reach its maximum height:

t = (v - u) / a

Since the rocket is moving upward, take the acceleration as negative (g = -9.8 m/s²).

t₁ = (112.8 m/s - 0 m/s) / (-9.8 m/s²)

t₁ = 11.51 s (approx)

Now, we can determine the maximum height reached by the rocket using the equation:

v² = u² + 2as

where
s = displacement

Since the rocket is moving upward, the final velocity is 0 m/s when it reaches the maximum height.

0² = (112.8 m/s)² + 2(-9.8 m/s²)s

-12698.88 m²/s² = -19.6 m/s² * s

s = -12698.88 m²/s² / -19.6 m/s²

s = 648.46 m (approx)

Now, we need to calculate the time taken for the rocket to fall from the maximum height to the ground.

Using the equation:

s = ut + 0.5at²

where
s = displacement (the height from the maximum height to the ground)
u = initial velocity
a = acceleration (g = 9.8 m/s², taken as positive)
t = time

The initial velocity is 0 m/s since it starts from rest at the maximum height.

648.46 m = 0 m/s * t + 0.5 * 9.8 m/s² * t²

648.46 m = 4.9 m/s² * t²

t² = 648.46 m / 4.9 m/s²

t² = 132.39 s²

t = √132.39 s

t ≈ 11.51 s

Thus, the time taken from the moment the rocket is launched until it strikes the ground is approximately 11.51 seconds.

To solve this problem, we can use the equations of motion.

Let's consider the upward motion of the rocket first. We know that the initial velocity (u) is 0 since the rocket is launched upward from a stationary position. The acceleration (a) is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2 in the downward direction. The displacement (s) is given as 225.6 m.

Using the equation of motion for displacement:
s = ut + (1/2)at^2

Substituting the known values:
225.6 = 0 + (1/2)(-9.8)t^2
225.6 = -4.9t^2

Rearranging the equation:
t^2 = 225.6 / -4.9

Taking the square root:
t = √(225.6 / -4.9)

Now, since time cannot be negative in this context, we can ignore the negative sign. Hence:
t = √(225.6 / 4.9)

Calculating this value, we get:
t ≈ 4.0 seconds

Therefore, the time taken for the rocket to reach its highest point is approximately 4 seconds.

Now, after the rocket's fuel is used up, it undergoes free fall. We know that the velocity at this instant is 112.8 m/s, and we need to find the time it takes for the rocket to strike the ground.

Using the equation of motion for velocity:
v = u + at

Substituting the known values:
112.8 = 0 + 9.8t

Simplifying the equation:
112.8 = 9.8t

Dividing both sides by 9.8:
t = 112.8 / 9.8

Calculating this value, we get:
t ≈ 11.5 seconds

Therefore, the time taken for the rocket to strike the ground after the fuel is used up is approximately 11.5 seconds.

Adding these two times together, we get the total time taken from the moment the rocket is launched until it strikes the ground:
Total time = 4 + 11.5
Total time ≈ 15.5 seconds