Question

Someone throws a ball upward with an initial velocity of v_i. Use the free fall equations to determine and show the final velocity v_f the ball has when it returns to the height from which it was released (hint you want a final equation that contains those two variables and no others). (further hint: what hidden information can you get from the phrase “returns to the height from which it was released”?) Ignore air resistance

Answer 1

From kinematics,

v² - u² = 2a$\Delta$x

where v is final velocity and u is initial velocity,

as final and initial heights are same

$\Delta$x = 0  

so,

v = u

Therefore,

v_f = v_i

we can say that final velocity will be same as the velocity with which it was thrown.