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.

being black

31 cos 35

35 To find the horizontal velocity component of the ball, we can use the basic trigonometric functions. The horizontal velocity component can be found by multiplying the initial velocity of the ball (31 m/s) by the cosine of the angle at which it was hit (35 degrees).

Horizontal velocity component = Initial velocity * Cos(angle)

Horizontal velocity component = 31 m/s * cos(35 degrees)

To calculate the value, we can use a scientific calculator that has a cosine function. Alternatively, we can use the following steps to solve it manually:

1. Convert the angle from degrees to radians, as trigonometric functions typically work with radians. To convert degrees to radians, we can use the formula: radians = degrees * (pi/180).

Angle in radians = 35 degrees * (pi/180) = 0.6109 radians (rounded to four decimal places).

2. Multiply the initial velocity by the cosine of the angle to find the horizontal velocity component.

Horizontal velocity component = 31 m/s * cos(0.6109 radians).

Using a scientific calculator or an online trigonometric calculator, we find that cos(0.6109 radians) is approximately 0.8147 (rounded to four decimal places).

Horizontal velocity component ≈ 31 m/s * 0.8147 ≈ 25.27 m/s (rounded to two decimal places).

Therefore, the horizontal velocity component of the ball is approximately 25.27 m/s (rounded to the nearest tenth of a m/s).