a golf ball is launched at a 37 degree angle from the horizontal at an initial velocity of 48.6 m/s. state the initial velocity in rectangular coordinates.

please show me how to figure this out

Vo = 48.6m/s @ 37deg.

Vo(h)=48.6cos37 = 38.8m/s = hor. comp.
Vo(v)=48.6sin37 = 29.2m/s = ver comp.

Rectangular Form:
Vo = 38.8 + j29.2 m/s.

The "j" means there is a 90 degree
phase difference between the 2 vectors.

To find the initial velocity in rectangular coordinates, you need to break down the given initial velocity of the golf ball into its horizontal and vertical components.

The horizontal component of the initial velocity, VX, can be calculated using the formula:
VX = V * cos(θ)
where V represents the magnitude of the initial velocity (48.6 m/s) and θ represents the launch angle (37 degrees).

So, the horizontal component of the initial velocity is:
VX = 48.6 m/s * cos(37°)

To find the vertical component of the initial velocity, VY, you can use the formula:
VY = V * sin(θ)
where V represents the magnitude of the initial velocity (48.6 m/s) and θ represents the launch angle (37 degrees).

So, the vertical component of the initial velocity is:
VY = 48.6 m/s * sin(37°)

Now, let's calculate these values:

VX = 48.6 m/s * cos(37°)
VX = 48.6 m/s * 0.7986
VX ≈ 38.84 m/s (rounded to two decimal places)

VY = 48.6 m/s * sin(37°)
VY = 48.6 m/s * 0.6018
VY ≈ 29.30 m/s (rounded to two decimal places)

Therefore, the initial velocity in rectangular coordinates is approximately VX = 38.84 m/s in the horizontal direction and VY = 29.30 m/s in the vertical direction.