Question

as a space rocket takes off vertically at 10ms-1 a lose bolt deattaches from rocket when it's height is 120m at what speed will it strike the ground​

Answer 1

Answer:

Since the bolt gets detached while the rocket is moving, it would have some initial velocity due to inertia. Hence the bolt would travel some height after which it reaches zero velocity. At this point it starts falling towards the ground under free fall.

The values required for calculation are:

• Initial Velocity (u) = Speed of Rocket = 10 m/s
• Final Velocity (v) = 0 m/s (At the highest point)
• Acceleration = - 10 m/s² (Since g acts downwards)

Now let's first calculate the distance travelled by the bolt after getting detached. Using the third equation of motion we get:

⇒ v² - u² = 2as

⇒ 0² - 10² = 2 (-10) s

(a = -10, since the gravity is acting downwards while the object is moving upwards.)

⇒ -100 = -20 s

⇒ s = 100/20 = 5 m

Hence the bolt has travelled 5 m from the initial point where it gets detached. Hence the bolt starts falling with zero initial velocity at 125 m.

At this point, the values are:

• Initial Velocity (u) = 0 m/s
• Height from ground (s) = 125 m
• Acceleration = + 10 m/s²

Now using third equation of motion again we get:

⇒ v² - 0² = 2 (10) (125)

⇒ v² = 2500

⇒ v = √2500

⇒ v = 50 m/s

Hence the bolt would strike the ground with a speed of 50 m/s.

Answer 2

Given :-

As a space rocket takes off vertically at 10ms-1 a lose bolt deattaches from rocket when it's height is 120m

To Find :-

At what speed will it strike the ground​

Solution :-

Since the space rocket is going downwards then it's acceleration will be -ve. As well as final velocity will be 0 because it stops by coming downwards

v² = u² + 2gh

(0)² = (10)² + 2(-10)(s)

0 = 100 + (-20)(s)

0 = 100 - 20s

0 - 100 = -20s

-100 = -20s

-100/-20 = s

5 = s

Now

Speed it will strike = final velocity

Distance = 120 + 5 = 125 m

Again by using same formula

v² = u² + 2gh

v² = 0² + 2(10)(125)

v² = 0 + 20 × 125

v² = 2500

v = √2500

v = 50 m/s

Know More :-

Initial velocity = It is defined as the velocity before the acceleration is applied.

Final velocity = It is defined as the velocity after the acceleration is applied.

Acceleration = Change in velocity with respect to time is called acceleration

Equations of motion

1st equation

v = u + at

2nd equation

s = ut + 1/2 at²

3rd equation

v² - u² = 2as

Where

v = final velocity

u = initial velocity

s = distance

t = time

a = acceleration