Peter is shooting arrows at a target with a bow. The target is 10m above the arrows launch point and some distance from Peter. If the arrows are shot with initial velocity Vo at 60 degrees with respect to the ground, then they will hit the target at the highest point of their trajectory. Find the initial speed of the arrows.

Y^2 = Y0^2 + 2g*h

Yo^2 = Y^2-2g*h = 0 + 19.6*10 = 196
Yo = 14 m/s = Ver. component of initial
velocity.

Yo = Vo*sin60 = 14 m/s.
Vo = 14/sin60 = 16.2m/s[60o]

To find the initial speed of the arrows, we can analyze the projectile motion of the arrows.

First, let's consider the vertical motion of the arrows. We know that the maximum height of the arrows' trajectory occurs when its vertical velocity component becomes zero. At this point, the arrows will be 10m above the launch point.

Using the formula for vertical displacement in projectile motion, we have:

Δy = Vyi * t + (1/2) * (-g) * t^2

Since the arrows are at their highest point, Δy = 10m and Vyi = 0. We can ignore the negative sign for gravity since we're dealing with magnitudes.

So we have:

10 = 0 * t + (1/2) * (-9.8) * t^2

Simplifying the equation, we get:

10 = -4.9 * t^2

Dividing both sides by -4.9, we get:

-2.04082 = t^2

Taking the square root of both sides, we find:

t ≈ 1.42857s

Now, let's consider the horizontal motion of the arrows. Since there is no horizontal acceleration, the arrows travel a distance d horizontally at a constant velocity for the time t.

Using the formula for horizontal displacement in projectile motion, we have:

Δx = Vxi * t

Since the arrows are launched at an angle of 60 degrees with respect to the ground, the horizontal component of their initial velocity is given by Vxi = Vo * cos(60°).

Now we can substitute the known values into the equation:

Δx = (Vo * cos(60°)) * t

We want to find Vo, so we solve for it:

Vo = Δx / (cos(60°) * t)

To find Δx, we need to consider the horizontal distance to the target. Let's assume the distance is D meters.

Now we substitute Δx = D into the equation:

Vo = D / (cos(60°) * t)

With values D = (the distance to the target) and t ≈ 1.42857s, you can now calculate the initial speed of the arrows.