A projectile launched from the ground explodes into three fragments of equal mass at the top point of the trajectory. One of the fragments lands t seconds after the explosion two other fragments land simultaneously 2 t seconds after the explosion. How high above the ground does the projectile explode? (take t =2 / 5 seconds and g =10 ~m / s ^2 )

Step-by-step solution

Let u s call h the height above the ground at which the projectile explodes and v_ k y (j=1,2,3) the y component of the velocity at the moment of the explosion for the three fragments. I will label with 1 the fragment which lands after t seconds. Since the landing time depends only on the y -component of the velocity at the moment of the explosion, we have: v_ 3 y =v_ 2 y . We then need only the equations for fragments 1 and 2 , stating that at landing time the y -coordinate will be equal to 0 : h+v_ 1 y t- g^2 2 =