Answer : The maximum height attained by the particle is 935 km.
Explanation :
The formula used for the maximum height attained by the particle is,
[tex]h=\frac{v^2}{2g-\frac{v^2}{R}}[/tex]
where,
h = height of the particle = ?
v = speed of the particle = [tex]4.0km/s=4.0\times 10^3m/s[/tex]
g = acceleration due to gravity = [tex]9.8m/s^2[/tex]
R = radius of earth = [tex]6400km=64\times 10^5m[/tex]
Now put all the given values in the above formula, we get:
[tex]h=\frac{(4.0\times 10^3m/s)^2}{(2\times 9.8m/s^2)-\frac{(4.0\times 10^3m/s)^2}{64\times 10^5m}}[/tex]
[tex]h=9.35\times 10^5m=935\times 10^3m=935km[/tex]
Therefore, the maximum height attained by the particle is 935 km.
