How high is the fence?

In summary: He jumped up and grabbed an apple that was on a roof, then ran back down and jumped up to the next roof and so on. The answer to the problem was that the thief traveled a total of 36.2 feet in the time it took him to grab the apple. 36.2 feet is more than 5 feet. So, while the golf ball in this example would go a long way, the apple would not. Ah. True. I'm not thinking, it's almost midnight here. Now that you mention it, it will go up a significant amount.
  • #1
sterlinghubbard
5
0
Homework help. (Solved)

A golf ball is hit at ground level. The ball is observed to reach its maximum height above ground level 4.3s after being hit. 1.2s after reaching this maximum height, the ball is observed to barely clear a fence taht is 309 ft from where it was hit. The accelerration of gravity is 32 ft/s^2. How high is the fence? Answer in units of ft.

The horizontal velocity is constant and 56.18 as defined as distance over time. The vertical velocity is variable but I found the instantaneous velocity (137.6) in an attempt to find the initial angle. I am stumped. I keep coming up with values around 200 ft and that doesn't seem possible.

[edit] Solution is 272.8 [/edit]
 
Last edited:
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  • #2
Could you show your work? If you show it we could probably point out what you did wrong.

But I assume you are using the basic mechanics equations? The one you probably would want to start with is v-final^2 = v-initial^2 + 2*g*h.
 
  • #3
A ball that rises for 4.3 seconds before reaching maximum height is going to go pretty high. In another 1.2 seconds it is not going to fall terribly far. You might feel better about your answer if you calculatied the maximum height of the ball as well as the height of the fence.
 
  • #4
OlderDan said:
A ball that rises for 4.3 seconds before reaching maximum height is going to go pretty high. In another 1.2 seconds it is not going to fall terribly far. You might feel better about your answer if you calculatied the maximum height of the ball as well as the height of the fence.

But it is not hit straight up, it is hit at an angle. If it is hit at a low enough angle, it could rise to only 10 feet in that time.

Ignore my previous post, i was wrong. You want v-final = v-initial + g*t. Calculate the inital vertical velocity and then you should be able to go from there. Assuming I didn't mess up again.
 
  • #5
WhirlwindMonk said:
But it is not hit straight up, it is hit at an angle. If it is hit at a low enough angle, it could rise to only 10 feet in that time.

Ignore my previous post, i was wrong. You want v-final = v-initial + g*t. Calculate the inital vertical velocity and then you should be able to go from there. Assuming I didn't mess up again.

Regardless of angle, you must have adequate vertical velocity in order to RISE for 4.3 seconds.
 
  • #6
whozum said:
Regardless of angle, you must have adequate vertical velocity in order to RISE for 4.3 seconds.

Ah. True. I'm not thinking, it's almost midnight here. Now that you mention it, it will go up a significant amount. sterlinghubbard, one thing you also want to think about is that books don't always have the most realistic answers. I remember a calc problem with a 6.5 foot tall thief running as fast as an olympic sprinter.
 

What is the maximum height a golf ball can reach?

The maximum height a golf ball can reach depends on various factors such as the initial velocity, launch angle, air resistance, and gravity. However, on average, a golf ball can reach a height of 70-100 feet.

What is the physics behind a golf ball's maximum height?

The physics behind a golf ball's maximum height can be explained by the laws of motion and the principles of aerodynamics. When a golf ball is hit with an initial velocity and launch angle, it experiences a force of gravity pulling it downwards and air resistance pushing it upwards. The combination of these forces determines the maximum height the ball can reach.

How does air density affect a golf ball's maximum height?

Air density plays a significant role in determining a golf ball's maximum height. As the air density increases, it creates more resistance, making it harder for the ball to travel upwards. On the other hand, lower air density allows the ball to travel higher. This is why golfers often hit the ball further in higher altitudes.

What is the ideal launch angle for a golf ball to reach its maximum height?

The ideal launch angle for a golf ball to reach its maximum height is between 35-45 degrees. This angle allows the ball to travel the furthest distance while also reaching its highest point. However, the launch angle may vary depending on the golfer's swing and the type of club used.

Can a golf ball's maximum height be affected by wind?

Yes, wind can significantly affect a golf ball's maximum height. A strong headwind can reduce the ball's maximum height, while a tailwind can increase it. Crosswinds can also affect the ball's trajectory and cause it to deviate from its intended path, resulting in a lower maximum height.

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