If a golf ball leaves a tee with an initial velocity of 80ft/sec at a 24.45 degree trajectory angle...?

Question

If a golf ball leaves a tee with an initial velocity of 80ft/sec at a 24.45 degree trajectory angle, calculate how far the golf ball should travel.
Use 32.15 ft/sec for acceleration due to gravity.

Please help me...I am so confused and I have no clue to even what formula to use and I cannot find the right one on google...or understand it...

thanks so much =]

Answer 1

The speed part of the velocity can be split into 2 components: the horizontal part and the vertical part.

The horizontal velocity is the part that is the same as if you were driving your golf cart down the flat golf course. To calculate distance, all you do is multiply your golf cart speed by time. So if you get the horizontal speed of the golf ball and multiply it by time, then you have your distance. The horizontal speed of the golf ball is:

cosine(24.45) * 80 = 72.83 ft/sec

So, all you have to do is multiply 72.83 by the time (in seconds) and you get your distance in feet.

But where do you get the time from you ask? good question -- here's how to get the time:

The *vertical* portion of the velocity takes the ball up, then back down. The time of flight can be calculated from this. The vertical velocity is:

sine(24.45) * 80 = 33.12 feet/sec

The ball is going up by 33.12 feet/sec but begin pulled down by gravity at rate of 32.15 feet/sec per second. In a little more than 1 second all of that vertical speed will be "used up" and the ball will start to fall back down. To be precise, it takes 33.12/32.15 = 1.03 seconds to reach the top of the arc, and double that to get back to the ground (2.06 seconds).

To finish:
72.83 ft/sec horizontal velocity times 2.06 seconds = 150.0 feet.

Note: this problem doesn't account for wind resistance, dimples on the ball, or bouncing on the green after the ball has landed. It is a simple physics problem, only.

Answer 2

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Answer 3

the answer above is correct, but to simplify, use the formula

range = (V^2 * sin (2*theta)) / g

where velocity is in ft/sec and accel due to grav is in ft/sec^2,

range = [80^2 * sin(2*24.45)] / 32.15
range = [6400*sin(48.9)] / 32.15
range = (6400*0.75356) / 32.15 = 150.00 feet