Question

A particle is fired vertically upward with a speed of 3.8km/s. Find the maximum height attained by the particle.

Answer 1

selected Nov 17, 2018 by faiz

 

Best answer

At the surface of the earth, the potential energy of the earth-particle system is GMm/R  with usual symbol. The kinetic energy is 1/2 mv2 where  v0 = 9.8km/s . At the maximum height the kinetic energy is zero. If the maximum height reached is H, the potential energy of the earth-particle system at this instant is -GMm/R+H. Using conservation of energy,

Writing GM=gR2 and dividing by m,

Putting the value of R,v0 and g on right side,

H = (27300 - 6400)km =20900km

Answer 2

The maximum height attained by the particle is 736 km.

Explanation:

Given that,

Initial speed of a particle, u = 3.8 km/s = 3800 m/s

We need to find the maximum height attained by the particle. At maximum height the final speed of the particle is equal to 0, v = 0

Let h is the maximum height attained. Using third equation of motion,

$v^2-u^2=2ah$

Here, a = -g

$-u^2=-2gh\\\\h=\dfrac{u^2}{2g}\\\\h=\dfrac{(3800)^2}{2\times 9.8}\\\\h=736734.69\ m\\\\h=736\ km$

So, the maximum height attained by the particle is 736 km. Hence, this is the required solution.

Learn more,

Third equation of motion

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