An object that is launched straight up from the ground reaches maximum height H

Question

An object that is launched straight up from the ground reaches maximum height H and falls straight back down to the ground, hitting it T seconds after launch. Neglect any effects due to air resistance. Express the average speed over the entire trip as a function of H and T. V_av = Express the average speed for the same interval of time as a function of the initial launch speed v_0 V_av = Use the definition of average speed as distance traveled divided by the elapsed time, and the expression for the average speed of an object when it is experiencing constant acceleration to express v_av in terms of v_0.

Explanation / Answer

given

   object launched straight up with initial speed of v0 and reaches maximum height H,

and falls straight down to the ground, hitting it T seconds after launch.

Neglecting any effects due to air resistance,

as the object reaches the max height it would have speed of zero and when it starts from max height to ground it will have same speed while reaching the ground

so the average speed of the object is

   V avg = Vo +V0/2
= 2 V0/2
= V0

so the average speed is V0

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