Find Min Proj Angle & Max Height of Golf Ball with Initial Speed of 91.1 m/s

In summary, a golf ball with an initial speed of 91.1 m/s landed 186 m downrange on a level course, with an acceleration of gravity of 9.8 m/s2. The minimum projection angle that would achieve this result, neglecting air friction, is 6.35 degrees. The maximum projection angle that would achieve this result cannot be determined without further information. The maximum height reached by the ball, using the angle determined in part A, cannot be determined without further information. The expert used the given information to calculate the minimum projection angle of 6.35 degrees. However, the maximum projection angle and maximum height cannot be determined without additional information.
  • #1
jtwilley
1
0
A golf ball with an initial speed of 91.1 m/s
lands exactly 186 m downrange on a level
course.
The acceleration of gravity is 9.8 m/s2 .

A)Neglecting air friction, what minimum pro-
jection angle would achieve this result?

Answer 6.35 minimum angle

B)Neglecting air friction, what maximum pro-
jection angle would achieve this result?


C)What is the maximum height reached by the
ball, using the angle determined in part A?


I have found the minimum angle but I can't seem to get the height and max angle correct.
 
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  • #2
Show your work. How did you get the minimum angle?

ehild
 

What is the initial speed of the golf ball?

The initial speed of the golf ball is 91.1 m/s. This is the starting velocity of the ball as it is hit by the golf club.

How do you find the minimum projection angle of the golf ball?

To find the minimum projection angle, you can use the equation θ = tan⁡⁡⁡⁡^-1⁡⁡⁡⁡(v₀^2/gR), where θ is the projection angle, v₀ is the initial speed, g is the acceleration due to gravity, and R is the range of the ball. Plug in the given values and solve for θ.

What is the maximum height of the golf ball?

The maximum height of the golf ball can be found using the equation h = (v₀^2 sin^2⁡θ)/(2g), where h is the maximum height, v₀ is the initial speed, θ is the projection angle, and g is the acceleration due to gravity. Plug in the given values and solve for h.

How does air resistance affect the results?

Air resistance can affect the results by slowing down the golf ball as it travels through the air. This can decrease the maximum height and range of the ball, and also change the optimal projection angle. However, for initial speeds as high as 91.1 m/s, the effect of air resistance is minimal and can be ignored in calculations.

Can the results be applied to all golf balls?

No, the results may vary for different types of golf balls due to differences in size, weight, and aerodynamics. These calculations are based on a standard golf ball and may not be accurate for all types of golf balls.

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