A particle is thrown vertically up with an initial velocity 9 ~m / s from the surface of Earth (take g=10 ~m / s ^2 ). The time (in s) taken by the particle to reach a height of 4 ~m from the surface second time (in seconds) is

Step-by-step solution

Time taken by the particle to reach a height h from the surface of Earth is obtained from h=u t- 1 2 g t^2 Here, u=9 ~m / s , h=4 ~m , g=10 ~m / s ^2 aligned & 4=9 t- 1 2 10 t^2 & 4=9 t-5 t^2 or 5 t^2-9 t+4=0 & 5 t^2-5 t-4 t+4=0 & 5 t(t-1)-4(t-1)=0 & t=1 ~s or t= 4 5 ~s aligned Hence, the time taken by the particle to reach a height of 4 ~m from the surface second time is 1 ~s .