asap need help with this projectile q (1 Viewer)

[medaspirant]

im getting answer as 1.16 but with some eq which i dont know a lot bout. like i researched and found this hang time equation:
t = 2vsintheta / g
and like others have also utilised this formula in their explanation but idk if it is correct. also if someone could tell me how this is derived and whether its like assumed / common knowledge this formula.
i saw this method in this website:
www. gauthmath.com/solution/1-A-projectile-is-launched-from-point-O-at-an-angle-of-22-circ-with-an-initial-v-1701876453272582
remove the space after www. for link to work

another method i saw is
brainly. in/question/12137403
remove space after brainly. for link to work

but i dont rlly understand so like if someone could guide me in how to approach this q it would be appreciated.

 

[Lith_30]

You can solve this question like finding the point of intersection between two graphs.

The relationship between the horizontal run and vertical rise of the incline plane is

For the projectile we know that and . Then to find the horizontal displacement of the projectile we use.

So now we want to find the value of time for which the rise and run of the incline plane is the same as the vertical and horizontal displacement of the projectile. To do this we solve both the equations for the incline plane and the horizontal displacement of the projectile simultaneously.



We know that so...



We're only interested in the second answer, so lets sub in the values for that answer.

 

[ExtremelyBoredUser]

im getting answer as 1.16 but with some eq which i dont know a lot bout. like i researched and found this hang time equation:
t = 2vsintheta / g
and like others have also utilised this formula in their explanation but idk if it is correct. also if someone could tell me how this is derived and whether its like assumed / common knowledge this formula.

Sure.


At the peak, the vertical velocity will be 0.


Rearranging variables.

Now the motion is clearly symmetrical, and therefore you can deduce that the time taken to reach the peak is equal to the time taken to reach the landing point, as it clearly lands on the same angle of elevation as it is launched from.

Hence;


another form of writing u_y

Substituting this


And hence the time equation.