If a .3kg arrow is fired at 120m/s at a 30degree angle with the horizontal, how high is it at the top of its arc? I'm confused. Do I break up the x and y components of velocity or do I set initial KE + PE = KE (top of arc)+ PE (top of arc) to get 1/2(.3)(120)*2+ 0 = 0 +.3(9.8)h and solve for h?

You need to break it into components.

viy=120sin30

vy at top=0=viy-gt so solve for time t to the top.

Htop= viy*t-1/2 g t^2

Thanks. Thought so but my friend disagreed with me.

Let your friend disprove me. It is possible to use energy, but you have to find the x component of velocity first anyway.

To determine the height of an arrow at the top of its arc, you can use the principle of conservation of mechanical energy. However, before we proceed, let's break up the components of velocity.

First, let's consider the horizontal component, which is given by:

Vx = V * cos(theta)

where V is the magnitude of the velocity (120 m/s in this case) and theta is the angle with the horizontal (30 degrees in this case).

Vx = 120 * cos(30)
Vx ≈ 103.92 m/s

Next, let's consider the vertical component, which is given by:

Vy = V * sin(theta)

Vy = 120 * sin(30)
Vy ≈ 60 m/s

Now, using the principle of conservation of mechanical energy, we can set the initial kinetic energy (KE) plus potential energy (PE) equal to the kinetic energy and potential energy at the top of the arc.

Initial KE + Initial PE = KE (top of arc) + PE (top of arc)

The initial kinetic energy is given by:

KE = 0.5 * mass * V^2

KE = 0.5 * 0.3 * (120)^2
KE ≈ 2160 J

The initial potential energy is zero since we can take the reference point at the ground level.

At the top of the arc, the arrow is momentarily at rest, so the kinetic energy is zero:

KE (top of arc) = 0 J

The potential energy at the top of the arc is given by:

PE (top of arc) = mass * g * height

where g is the acceleration due to gravity (9.8 m/s^2) and height is the height at the top of the arc (what we're trying to find).

Substituting in the values:

2160 J + 0 J = 0 J + 0.3 * 9.8 * height

Simplifying the equation:

2160 J = 2.94 * height

Now we can solve for the height:

height = 2160 J / 2.94
height ≈ 734.69 m

Therefore, the height of the arrow at the top of its arc is approximately 734.69 meters.