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 horizontal velocity component of the ball? Round the answer to the nearest tenth of a m/s
To find the horizontal velocity component of the ball, we need to use trigonometry and the given information: the initial velocity of the ball (31 m/s) and the launch angle (35 degrees).
The horizontal velocity component of the ball can be calculated using the formula:
Horizontal Velocity = Initial Velocity * Cos(Launch Angle)
1. Convert the launch angle from degrees to radians:
- To convert from degrees to radians, multiply the angle by π/180 (approximately 0.01745).
Launch Angle in Radians = 35° * (π/180) ≈ 0.6109 radians
2. Calculate the horizontal velocity component:
- Substitute the values into the formula:
Horizontal Velocity = 31 m/s * cos(0.6109 radians)
Using a calculator:
Horizontal Velocity ≈ 31 m/s * cos(0.6109) ≈ 31 m/s * 0.811 ≈ 25.1 m/s
Therefore, the horizontal velocity component of the ball is approximately 25.1 m/s (rounded to the nearest tenth).