The distance that the golf ball travels down the fairway can be determined using the horizontal and vertical components of its initial velocity.
To find the horizontal component, we can use the formula:
horizontal velocity = initial velocity * cos(angle)
where the angle is the angle the ball makes with the horizontal, which in this case is 25°.
Plugging in the values, we get:
horizontal velocity = 180 ft/sec * cos(25°)
To find the vertical component, we can use the formula:
vertical velocity = initial velocity * sin(angle)
Plugging in the values, we get:
vertical velocity = 180 ft/sec * sin(25°)
Since the ball hits the ground, the vertical displacement will be equal to zero. We can use the formula:
vertical displacement = initial vertical velocity * time + 0.5 * acceleration * time^2
where the acceleration is the acceleration due to gravity, which is approximately -32 ft/sec^2. Solving for time, we get:
0 = initial vertical velocity * time + 0.5 * acceleration * time^2
Plugging in the values, we get:
0 = 180 ft/sec * sin(25°) * time + 0.5 * -32 ft/sec^2 * time^2
We can solve this quadratic equation to find the time it takes for the ball to hit the ground.
Once we have the time, we can find the horizontal displacement using the formula:
horizontal displacement = horizontal velocity * time
Plugging in the values, we get:
horizontal displacement = 180 ft/sec * cos(25°) * time
Calculating the values for time and horizontal displacement will give us the answer to the question.
Note: Since the equation is quadratic, there will be two possible times when the ball hits the ground. We need to choose the positive value for time since time cannot be negative in this context.