Final answer:
The golf ball travels approximately 211.68 meters horizontally before reaching the fairway.
Step-by-step explanation:
To determine the horizontal distance traveled by the golf ball, we first need to find its horizontal velocity.
This can be found by multiplying the initial velocity of the ball (49 m/s) by the cosine of the launch angle (30°).
Vx = 49 m/s * cos(30°)
= 42.43 m/s
Next, we need to find the time it takes for the ball to reach the fairway. We can use the equation:
t = d / Vx
where t is the time, d is the horizontal distance, and Vx is the horizontal velocity.
Rearranging the equation, we have:
d = t * Vx
Since the ball is launched at an angle above the horizontal, it will take the same amount of time to reach the highest point in its trajectory as it will to reach the same height on the way down.
So, we can find the time by dividing the total flight time by 2.
The total flight time can be determined using the equation:
t = (2 * Vy) / g
where Vy is the vertical component of the initial velocity and g is the acceleration due to gravity (9.8 m/s²).
Using the initial velocity (49 m/s) and launch angle (30°), we can find Vy by multiplying the initial velocity by the sine of the launch angle:
Vy = 49 m/s * sin(30°)
= 24.5 m/s
Finally, plugging in the values, we have:
t = (2 * 24.5 m/s) / 9.8 m/s²
= 4.98 s
Using this value for t, we can find the horizontal distance traveled by the ball:
d = 4.98 s * 42.43 m/s
= 211.68 m
Therefore, the golf ball travels approximately 211.68 meters horizontally before reaching the fairway.