A space aircraft is launched straight up. The aircraft motor provides a constant acceleration for 10seconds, then the motor stops. The aircraft's altitude 15seconds after launch is 2km. Ignore air friction.

Determine (i) the acceleration, (ii)the maximum speed reached in km/h, (iii) the speed(in km/h) of the aircraft as it passes through a cloud 4km above the ground.

what is your question on this multistep problem?

To solve this problem, we need to use the equations of motion under constant acceleration.

Let's define the following variables:
a = acceleration
t = time
u = initial velocity
v = final velocity
s = displacement (altitude in this case)

(i) To find the acceleration, we can use the equation:

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

Given that the aircraft's altitude is 2 km after 15 seconds, we can substitute the values:

2 km = 0 + (1/2)a(15)^2

simplifying:

2 km = (225/2)a

Dividing both sides by (225/2):

a = (4/225) km/s^2

So, the acceleration is (4/225) km/s^2.

(ii) To find the maximum speed, we can use the equation:

v = u + at

Since we know that the motor provides a constant acceleration for 10 seconds, we can substitute the values:

v = 0 + (4/225) km/s^2 * 10 s

Simplifying:

v = (40/225) km/s

To convert km/s to km/h, we multiply by (60*60) since there are 60 seconds in a minute and 60 minutes in an hour:

v = (40/225) km/s * (60*60) s/h

Simplifying:

v = (1600/225) km/h

So, the maximum speed reached is approximately 7.11 km/h.

(iii) To find the speed as it passes through a cloud 4 km above the ground, we can use the equation:

v^2 = u^2 + 2as

Given that the displacement (altitude) is 4 km, we can substitute the values:

v^2 = 0 + 2 * (4 km) * (4/225) km/s^2

Simplifying:

v^2 = (32/225) km^2/s^2

To convert km^2/s^2 to km^2/h^2, we multiply by (60*60)^2:

v^2 = (32/225) km^2/s^2 * (60*60)^2 s^2/h^2

Simplifying:

v^2 = (32/225) km^2/h^2

Taking the square root of both sides:

v ≈ 2.377 km/h

So, the speed of the aircraft as it passes through the cloud 4 km above the ground is approximately 2.377 km/h.