A particle is projected from the surface of the earth with an initial speed of 4.0 kms ⁻¹ . The maximum height (in km) attained by the particle is _____ [Radius of earth =6400 ~km and g =9.8 ~ms ⁻² ]

Step-by-step solution

Using conservation of mechanical energy. Decrease in kinetic energy = Increase in gravitational potential energy array ll & 1 2 m v^2= U & 1 2 m v^2= m g h 1+ h R & h= v^2 2 g- v^2 R array Substituting the values, we get aligned h & = (4.0 10^3 )^2 2 9.8- (4 10^3 )^2 6.4 10^6 & =9.35 10^5 ~m =935 ~km aligned