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.
To find the vertical velocity component of the golf ball, we need to determine the component of the initial velocity in the vertical direction.
Given:
Initial velocity (v₀) = 31 m/s
Launch angle (θ) = 35 degrees
The vertical velocity component (vᵥ) can be calculated using the formula:
vᵥ = v₀ * sin(θ)
Using this formula, substitute the given values:
vᵥ = 31 m/s * sin(35°)
To find the answer, we need to calculate the sine of 35 degrees and multiply it by 31 m/s.
Calculating sin(35°), we get approximately 0.574.
Substituting this value into the formula:
vᵥ = 31 m/s * 0.574
Calculating the product, we find:
vᵥ ≈ 17.8 m/s
Therefore, the vertical velocity component of the golf ball is approximately 17.8 m/s.