Calculating Distance and Height of Ball w/ 18° Loft & 10.9s Air Time

In summary, to calculate the distance a ball travels when hit with a wood lofted at 18 degrees for 10.9 seconds, use the equation deltaX=Vx(deltaT) with an initial velocity of 18.5 m/s. To find the maximum height of the ball, use the equation for vertical motion with an initial velocity of 18.5 m/s and an acceleration of 9.8 m/s^2.
  • #1
@d@m
2
0

Homework Statement


If a wood with loft 18 degrees is used to hit a ball that is in the air for 10.9 s, calculate:
(a) The distance the ball travels if its intial velociity is 18.5 m/s.
(b) The maximum height of the ball


Homework Equations





The Attempt at a Solution

 
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  • #2
@d@m said:

Homework Statement


If a wood with loft 18 degrees is used to hit a ball that is in the air for 10.9 s, calculate:
(a) The distance the ball travels if its intial velociity is 18.5 m/s.
(b) The maximum height of the ball


Homework Equations





The Attempt at a Solution


For a:
If you know the time in which the ball is in the air for you can easily find the horizontal range. You do this because you know the initial velocity, which is 18.5 m/s [18 deg above the horizontal]. You can calculate the horizontal speed, which is always constant in this case. Then use the equation deltaX=Vx(deltaT) to find the horizontal range...

For b:
Time is independent of the vertical and horizontal directions so you can use the same time in the vertical calculations... You know acceleration in the y direction (9.8), You know the initial speed in the y direction because you can easily calculate it... And if you want to know the maximum height of the ball you know that it's speed at the top of its flight will be 0... Now you have 3 pieces of info you can use to solve b...

Hope I helped...
 
  • #3


(a) To calculate the distance the ball travels, we can use the equation d = v*t, where d is the distance, v is the initial velocity, and t is the time. Plugging in the given values, we get d = (18.5 m/s)*(10.9 s) = 201.65 m. Therefore, the ball travels a distance of 201.65 meters.

(b) To calculate the maximum height of the ball, we can use the equation h = v^2*sin^2(theta)/(2*g), where h is the maximum height, v is the initial velocity, theta is the loft angle, and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the given values, we get h = (18.5 m/s)^2*sin^2(18 degrees)/(2*9.8 m/s^2) = 21.24 m. Therefore, the maximum height of the ball is 21.24 meters.
 

What is the formula for calculating the distance and height of a ball with 18° loft and 10.9s air time?

The formula for calculating the distance and height of a ball with 18° loft and 10.9s air time is:
Distance = (initial velocity * cos(angle) * air time)
Height = (initial velocity * sin(angle))^2 / (2 * gravity) + (initial velocity * sin(angle) * air time)

How do you determine the initial velocity of the ball?

The initial velocity of the ball can be determined by dividing the distance by the cosine of the angle and the air time. This will give you the initial horizontal velocity. Then, to find the initial vertical velocity, you can use the formula:
initial vertical velocity = (horizontal velocity * tan(angle)) - (gravity * air time / 2)

What is the value of gravity used in the calculation?

The value of gravity used in the calculation is typically 9.8 m/s^2. However, this may vary depending on the location and altitude.

How do you convert the calculated height from meters to feet?

To convert the calculated height from meters to feet, you can use the conversion factor of 3.281. Multiply the calculated height in meters by 3.281 to get the height in feet.

Can this formula be used for any angle and air time?

Yes, this formula can be used for any angle and air time as long as the initial velocity and gravity are known. However, it is important to note that the assumptions made in this formula may not be accurate for all situations, such as air resistance and the effects of spin on the ball.

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