I on finding seconds from maximum height.

[Sneakatone]

A human cannonball was fired from a cannon with a muzzle velocity of 107 km/h. The firing angle was 45 degrees from the horizontal


Ive converted 107 km/h to 29.71 m/s
1.How many seconds did it take for the human cannonball to reach maximum height?

2.How high did he rise?
h = (V²/4g)=22.5m
3.How far from the cannon did he land?
R = (V²/g) =29.72^2/9.8=90.1m


I cannot seem to find the time for #1 , i tried v/g=29.72/9.8=3.029 and that's wrong,
t = (V/g)√2= 4.28 and that is wrong.
what do I need to do

 

[NascentOxygen]

A human cannonball was fired from a cannon with a muzzle velocity of 107 km/h. The firing angle was 45 degrees from the horizontal


Ive converted 107 km/h to 29.71 m/s
1.How many seconds did it take for the human cannonball to reach maximum height?

You'd be seeking the time that passes until the vertical component of his velocity equals 0.

2.How high did he rise?
h = (V²/4g)=22.5m

What equation of motion did you apply here?

 

[Sneakatone]

I forgot but I got 2 and 3 correct, Is there a specific equation for 1?

 

[Yosty22]

Think about what max height means. As stated above, at the maximum height, the x-component of the velocity is ZERO. Try using an equation of velocity with respect to time and keep in mind that at the maximum height, the velocity is equal to 0. Plug that into the equation along with all other known variables and solve.

 

[Sneakatone]

would the angle be a factor when finding time?
I used v = gt + vi which ended up to v/g=t -> 29.72/9.81=3.029s but it is incorrect

 

[Yosty22]

I'm not completely sure, but I assume if you use the equation V_x=V_0x+a_xt and break V_0x into the component V_x=V₀cos\theta you can make the equation:
V_x=Vocos(/theta)+a_xt, you can make V_x zero, plug in the rest, then solve for t.

 

[NascentOxygen]

would the angle be a factor when finding time?
I used v = gt + vi which ended up to v/g=t -> 29.72/9.81=3.029s but it is incorrect

The equation is correct, but it applies to only the vertical component of velocity.