A golfer tees off and hits a golf ball at a speed of 31 m/s and at an angle of 35 degrees. What is the vertical velocity component of the ball? Round the answer to the nearest tenth of a m/s.

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To find the vertical velocity component of the golf ball, we need to use trigonometry based on the angle provided. The vertical velocity component can be determined by multiplying the total velocity of the ball by the sine of the angle.

First, we find the vertical velocity component (vₓ) using the formula:

vₓ = v * sin(θ)

Where:
v is the total velocity of the ball (31 m/s)
θ is the angle at which the ball was hit (35 degrees)

Now, substituting the given values into the equation:

vₓ = 31 m/s * sin(35 degrees)

Using a calculator or an online trigonometric calculator, we evaluate the sine of 35 degrees:

sin(35 degrees) ≈ 0.574

Now, substitute this value into the equation:

vₓ = 31 m/s * 0.574

Calculating this expression, we find:

vₓ ≈ 17.79 m/s

Therefore, the vertical velocity component of the golf ball is approximately 17.8 m/s (rounded to the nearest tenth).