Question

Three objects are dropped from the top of a building. The first is thrown straight down with a velocity v, the second is thrown straight up with a velocity 2v, and the third is simply dropped. Which one has the highest speed when it hits the ground?

Answer 1

Second ball

Step-by-step explanation:

When a ball is thrown up with a certain velocity when the object reaches the same point from where it was thrown the velocity of the object becomes equal to the velocity with which the ball was thrown.

First ball

`v_g_1^2-u^2=2as\\\Rightarrow v_g_1=√(2as+u^2)\\\Rightarrow v_g_1=√(2as+v^2)`

Second ball

`v_g_2^2-u^2=2as\\\Rightarrow v_g_2=√(2as+u^2)\\\Rightarrow v_g_2=√(2as+4v^2)`

Third ball

`v_g_3^2-u^2=2as\\\Rightarrow v_g_3=√(2as+0^2)\\\Rightarrow v_g_3=√(2as)`

From the equations above it can be seen that the second ball will have the highest velocity when it hits the ground.

So,
`v_g_3<v_g_1<v_g_2`