A 7400 kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.35 m/s^2 and feels no appreciable air resistance. When it has reached a height of 585 mm, its engines suddenly fail so that the only force acting on it is now gravity. Required:
a. What is the maximum height this rocket will reach above the launch pad?
b. How much time will elapse after engine failure before the rocket comes crashing down to the launch pad, and how fast will it be moving just before it crashes?
c. Sketch ayât,,vyâât, and y - t graphs of the rocketâs motion from the instant of blast-off to the instant just before it strikes the launch pad.

Explanation:

Let us first calculate the velocity of rocket on reaching the height of 585 m

v² = u² + 2 a s

= 0 + 2 x 2.35 x 585

v = 52.43 m /s

For onward journey of rocket , initial velocity u = 52.43 m /s , acceleration = - g = - 9.8 m /s² final velocity at top point v = 0

v² = u² - 2gh

0 = 52.43² - 2 x 9.8 x h

h = 140.25 m

Total height reached

= 585 + 140.25

= 725.25 m

b )

Time to reach the top position be t₁

v = u - gt₁

0 = 52.43 - 9.8 t₁

t₁ = 5.35 s

Time to reach the ground after reaching highest point be t₂

h = ut + 1/2 g t²

u = 0 as at top point , velocity = 0

725.25 = 0 + .5 x 9.8 t₂²

t₂² = 148

t₂ = 12.16 s

Total time = t₁ + t₂

= 5.35 + 12.16

= 17.51 s .

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.