Question

the object thrown vertically upward reaches a height of 800m . what was it's initial velocity? how long will the object take to come back to the earth? assume g =10m/s​

Answer 1

Given that, an object thrown vertically upward reaches a height of 800m and acceleration due to gravity is 10 m/s².

We have to find the initial velocity of the object and the total time taken by the object.

From above data we have; s is 800 m, v is 0 m/s and a is -10 m/s² (as it is against the motion)

Now, using the Third Equation Of Motion i.e. v² - u² = 2as

Substitute the known values in the above formula,

→ (0)² - (u)² = 2(-10)(800)

→ - u² = -16000

→ u = 126.5

Therefore, the initial velocity of the object is 126.5 m/s.

Now, Using the First Equation Of Motion i.e. v = u +at

Substitute the known values,

→ 0 = 126.5 + (-10)(t)

→ -126.5 = -10t

→ 12.65 = t

→ 13 = t (approx.)

Total time taken by the object = (13 + 13)s = 26 s

Answer 2

━━━━━━━━━━━━━━━━━━━━

✴ Required Answer:

✒ GiveN:

• Height to which the object is thrown = 800 m
• Acceleration = - 10 m/s (Thrown upward)
• Final velocity = 0 m/s

✒ To FinD:

• Initial velocity of the object?
• Time taken to come back to earth?

━━━━━━━━━━━━━━━━━━━━

✴ How to solve?

To solve the above question, we need to have a basic knowledge about displacement, final and initial velocity, acceleration. After, that we should know the three equations of motion,

• v = u + at
• s = ut + 1/2 at²
• v² = u² + 2as

⚠️ These three equations of motion are used when acceleration is constant/uniform. Here, in case of free fall, the gravitational force is only acting upon the object. It means, the acceleration is the acceleration due to gravity. It is constant and we can use it here.

━━━━━━━━━━━━━━━━━━━━

✴ Solution:

We have,

• Acceleration = - 10 m/s
• Height/Displacement = 800 m
• Final velocity = 0 m/s

(The velocity will gradually decrease because direction of acceleration is opposite to the direction of velocity.)

Using 3rd equation of motion,

➙ v² = u² + 2as

➙ 0² = u² + 2 × (-10) × 800

➙ u² = 16000

➙ u = 16000 m/s

➙ u = 40√10 m/s

➙ u = 126.49 m/s (approx.)

✒ Therefore, Initial velocity = 126.49 m/s.

Using 1st equation of motion,

➙ v = u + at

➙ 0 = 40√10 + (-10)t

➙ 10t = 40√10

➙ t = 4√10 s

↗️ Now, we know that the time required to go up is same as the time required to go down$.$

➙ Total time taken = Time of ascent + Time of descent

➙ Total time taken = 2 × 4√10 s

➙ Total time taken = 8√10 s

➙ Total time taken = 25.3 s (approx.)

✒ Therefore, total time taken to reach earth = 25.3 m/s

✳ Hence, solved!

━━━━━━━━━━━━━━━━━━━━