A ball is shot from the ground into the air

[Kpgabriel]

Homework Statement

A ball is shot from the ground into the air. At a height of 8.8 m, the velocity is observed to be

v = (7.4)i + (5.7)j in meters per second (i horizontal, j upward). To what maximum height will the ball rise?

Homework Equations

V^2 = Vi^2 + 2a(Δy)

The Attempt at a Solution

I have listed my knowns for x and y
Y:
Yi = 0m
Y = 8.8 m
V = 5.7 m/s
Vi = 11.8 m/s ~solved from the equation

X:
V = 7.4 m/s
Xi = 0m

I am having a difficult time finding the max height because they do not give the time and I am not sure if I could solve for time with only the y components.

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[billy_joule]

You don't need the time.
You can use the same equation again.
What is the y velocity when max height is reached?

 

[Kpgabriel]

You don't need the time.
You can use the same equation again.
What is the y velocity when max height is reached?

The velocity would be zero but I used that number and I get 7.1 m for displacement and that's too low.

 

[Kpgabriel]

The velocity would be zero but I used that number and I get 7.1 m for displacement and that's too low.

I see what I was doing wrong. I was forgetting to put in the 8.8 m and the 5.7 velocity which they already gave to me. Instead, I was using the initial velocity that I found which was not necessary.

 

[billy_joule]

As long as you recognise the starting points are different you can use either velocity, the answer is the same.