Question

Example 9 A particle is projected from the surface of earth wl an initial speed of 4.0 km/s. Find the maximum height attained by the particle. Radius of earth 6400 km, and g 9.8m/s

Answer 1

Answer : The maximum height attained by the particle is 935 km.

Explanation :

The formula used for the maximum height attained by the particle is,

`h=(v^2)/(2g-(v^2)/(R))`

where,

h = height of the particle = ?

v = speed of the particle =
`4.0km/s=4.0* 10^3m/s`

g = acceleration due to gravity =
`9.8m/s^2`

R = radius of earth =
`6400km=64* 10^5m`

Now put all the given values in the above formula, we get:

`h=((4.0* 10^3m/s)^2)/((2* 9.8m/s^2)-((4.0* 10^3m/s)^2)/(64* 10^5m))`

`h=9.35* 10^5m=935* 10^3m=935km`

Therefore, the maximum height attained by the particle is 935 km.