A ball is thrown vertically upwards with a velocity of 50 m/s. calculate (a) the maximum height to which it rises.
(b) the total time it takes to return to the surface of earth. (take g =10 m/s2 )

Given, For a vertically thrown upward,

          Initial velocity (u) = 50m/s

          Final velocity (v) = 0m/s { ∵ the body is thrown vertically upward }

          Acceleration due to gravity(a) = -(g)= -10m/s²

          Height reached (h) = ? , Time taken (t) = ?

We know that,v² = u²+2as

           or,        0² = (50)²+2×(-10)×h      { ∵ s=h }

           or,        0   = 2500+(-20h)

           or,        0   = 2500-20h

           or,        20h  = 2500

           or,        h   =

                  ∴     h   = 125metres

Also,       v  =  u + at

      or,    0  =  50+(-10)×t

      or,    0  = 50-10t

      or,    10t = 50

      or,    t   =

              ∴   t   = 5seconds   ANS

Hence, The height reached by the ball is 125m and time taken is 5secs.

the area between the graph and the t axis