Calculate Hang Time of 2D Projectile Motion - TS

[ThetaPi]

Could someone kindly explain to me what hang time is, in the context of 2D projectile motion? Enlighten me on the equations of motion that might be applicable to such a problem.

In other words, given a projectile launched at $$\theta$$ above the horizontal with an initial velocity of $$v_0$$, how do we calculate the hang time?

Thoughts. We need to calculate the time it takes for the projectile to reach the maximum height of the trajectory ($$t_1$$), and the time it takes to hit the ground after attaining its maximum height ($$t_2$$), and then add up $$t_1+t_2$$. I think that it will be convenient to use the y-component of $$v_0$$.

The maximum height of the trajectory is $$|1/2gt_2^2|$$. We can use this in the equation $$s_y=v_{0y}t_1-1/2gt_1^2$$ to find $$t_1$$.

I am rather confused...some posts I saw while browsing the forums said that the initial velocity does not affect the "hang time".

Thank you
TS

 

[dacruick]

velocity in the x-direction doesn't have an affect on hang time. hang time to me is simply the time that the projectile is in the air.

 

[ThetaPi]

I know that, but how do we calculate that numerically?

I presume that hang time is dependent on the y-component of the initial velocity?

Thanks again.

 

[dacruick]

right. you've written the equation that is going to give you the answer. If it is a projectile starting and stopping at the same y value, you know that maximum height has to be at half the total time its in the air. try working through it you seem to understand the concept