# How far away will the ball land?

• 1irishman
In summary, the ball rolls off an incline at a velocity of 22m/s. The angle of the incline is 32deg, and the height of the incline from the floor is 9m. Assume no air resistance.
1irishman

## Homework Statement

A ball rolls off an incline at a velocity of 22m/s. The angle of the incline is 32deg, and the height of the incline from the floor is 9m. Assume no air resistance.

d=vit+1/2at^2

## The Attempt at a Solution

I figured i should attempt to separate the motion of the ball into the x and y dimensions first so this was my attempt:
y motion
---------
22sin32*=11.7m/s
d=9m
vf=17.7m/s
a=-9.8
t=0.74

x motion
----------
vi=vf=18.7m/s because 22cos32=18.7m/s
t=0.74s

1irishman said:
y motion
---------
22sin32*=11.7m/s
d=9m
vf=17.7m/s
a=-9.8
t=0.74
How did you solve for the time?

time
-----
9=11.7t+1/2(-9.8)t^2
9=11.7t - 4.9t^2
-2.7/-4.9=.55
sqrt .55=.74s

1irishman said:
time
-----
9=11.7t+1/2(-9.8)t^2
Careful: Check the sign of your 'd' and 'vi'.

oops...I guess 'd' is -9 because it is pointing down? And 'vi' is -11.7 because of direction too?
I got a new time of .64s
If the above is correct, i still don't know how to solve this problem...help please? Thank you.

1irishman said:
oops...I guess 'd' is -9 because it is pointing down? And 'vi' is -11.7 because of direction too?
Yes.
I got a new time of .64s
My answer is close to that.
If the above is correct, i still don't know how to solve this problem...help please?
Now consider the horizontal motion. You have the speed and the time.

d=vt
So, d= (18.7)0.64
= 11.9m
Is that correct for distance?

1irishman said:
d=vt
So, d= (18.7)0.64
= 11.9m
Is that correct for distance?
That's the correct method. My answer is a bit less; try doing the calculation with more accuracy until the end.

Yes okay thank you, because it looks like the answer in the book is around 0.9 metres less than my value. How do i calculate with more accuracy throughout in the future please?

1irishman said:
How do i calculate with more accuracy throughout in the future please?
Just carry all intermediate values with more digits. Round off only at the end. For example, instead of 22sin32 = 11.7, use 11.66. And so on.

Doc Al said:
Just carry all intermediate values with more digits. Round off only at the end. For example, instead of 22sin32 = 11.7, use 11.66. And so on.

Thank you for all your help! I can see where my answers have been off marginally on previous problems due to rounding off the intermediate values too soon as it were.

## 1. How do you calculate the distance the ball will travel?

The distance a ball will travel can be calculated using the formula: d = v2sin(2θ)/g, where d is the distance, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

## 2. What factors affect the distance a ball will travel?

The distance a ball will travel is affected by factors such as the initial velocity, launch angle, air resistance, and the force of gravity. Other factors like wind, surface conditions, and the shape of the ball can also have an impact on the distance.

## 3. Is the distance the ball will travel the same every time?

No, the distance a ball will travel can vary depending on the factors mentioned above. Even small changes in the initial velocity or angle can result in a significant difference in the distance the ball travels.

## 4. Can you accurately predict the distance a ball will travel?

While the distance a ball will travel can be estimated using mathematical equations, there are always external factors that can affect the actual distance. Therefore, it is difficult to accurately predict the exact distance a ball will travel in real-life scenarios.

## 5. Can the distance a ball will travel be affected by the type of ball used?

Yes, the type of ball can play a role in the distance it will travel. For example, a heavier ball may not travel as far as a lighter one when thrown with the same force. Additionally, the shape and aerodynamic properties of the ball can also impact its distance.

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