Final answer:
To find the maximum height of the golf ball, we can use the equations of projectile motion. By finding the initial velocity using the given horizontal distance and launch angle, we can then calculate the maximum height. Using the formulas, the maximum height is approximately 95.1 m.
Step-by-step explanation:
To find the maximum height the golf ball will reach, we can use the equations of projectile motion. The maximum height can be determined using the formula:
h = (v^2 * sin^2(θ)) / (2 * g)
Where:
- h is the maximum height
- v is the initial velocity of the ball
- θ is the launch angle
- g is the acceleration due to gravity
Given that the ball can be hit a horizontal distance of over 300 m and is launched at an angle of 25 degrees, we need to find the initial velocity. We can use the formula:
d = (v^2 * sin(2θ)) / g
Where:
- d is the horizontal distance
- θ is the launch angle
- g is the acceleration due to gravity
Given that d = 300 m and θ = 25 degrees, we can rearrange the formula to solve for v:
v = sqrt((d * g) / sin(2θ))
After substituting the values, we can calculate the initial velocity:
v = sqrt((300 * 9.8) / sin(2 * 25)) ≈ 109.3 m/s
Now, we can use this initial velocity to calculate the maximum height:
h = (v^2 * sin^2(θ)) / (2 * g) = ((109.3^2) * sin^2(25)) / (2 * 9.8)
After evaluating this expression, the maximum height of the golf ball is approximately 95.1 m.