How Far Does the Ball Travel Horizontally Before Bouncing?

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In summary, the ball is thrown with an initial speed of 4.6m/s at an angle of 15(degrees) below the horizontal and is released 0.80m above the floor. The horizontal distance covered before bouncing is approximately 1.3m.
  • #1
kman2027
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A ball is thrown with an initial speed of 4.6m/s at an angle of 15(degrees) below the horizontal. It is released 0.80m above the floor.

What horizontal distance does the ball cover before bouncing?



I keep getting 2.4m as my answer, but it's wrong!
Here's what I did (Please correct any mistakes):


4.6sin(15) = initial vertical velocity = 1.19m/s

1.19^2 = 2gh

1.42 = 2gh

1.42/(2*9.81)=h= .072m

upward time = 1.19 m/s - gt = 0
1.19/9.81 = t = .121sec

total height = .072 + 0.8 = .872m

0.872 = 1/2gt^2
0.872/4.9 = t^2 = 0.178, sqrt = t = 0.422sec

total time = 0.121 + 0.422= 0.543sec

horizontal velocity = 4.6cos(15) = 4.44m/s

4.44x 0.543 = 2.41m (answer)
 
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  • #3
Remember that gravity acts on the object as soon as it is released, so the time it is in the air is dependent on that, regardless of how fast you're throwing it in the horizontal direction.
 
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  • #4
A ball is thrown with an initial speed of 4.6m/s at an angle of 15(degrees) below the horizontal. It is released 0.80m above the floor.

What horizontal distance does the ball cover before bouncing?

Is the answer 2.98?

Here's what I did:
4.6sin(15) = initial vertical velocity = 1.19m/s
horizontal velocity = 4.6cos(15) = 4.44m/s


.8/(1.19m/s)=.672s
0+(4.44m/s)(.672s)=2.98
 
  • #5
hi kman2027! :smile:
kman2027 said:
.8/(1.19m/s)=.672s
0+(4.44m/s)(.672s)=2.98

the first equation assumes that the vertical speed is constant (s = ut), it isn't :redface:

you need to use one of the standard https://www.physicsforums.com/library.php?do=view_item&itemid=204" equations to find t

(and then your method in the second equation is correct, since the horizontal speed is constant :wink:)
 
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  • #6
I got 1.7m this time.

I picked the constant acceleration equation:

y=yo+voyt-1/2gt^2
plugged in 0=.8+1.19t-1/2(-9.8)t^2
t=.385

(.385)(4.44)=1.7m

Is 1.7m right?
 
  • #7
hi kman2027! :smile:

(just got up :zzz: …)
kman2027 said:
plugged in 0=.8+1.19t-1/2(-9.8)t^2

not quite …

the initial vertical speed is negative :wink: …

(and you shouldn't have both those minuses in the t2 term)
kman2027 said:
A ball is thrown with an initial speed of 4.6m/s at an angle of 15(degrees) below the horizontal.
 
  • #8
My bad, I had a typo in the equation.

.8-1.19t+(1/2)(-9.8)t^2=0
t= .3s

Then:
(4.44)(.3)= 1.3m

Is 1.3m it?

Thanks for your help by the way!
 
  • #9
kman2027 said:
My bad, I had a typo in the equation.

.8-1.19t+(1/2)(-9.8)t^2=0
t= .3s

Then:
(4.44)(.3)= 1.3m

Is 1.3m it?

Thanks for your help by the way!

What's the equation for calculating distance based on velocity and time?
 
  • #10
yes 1.3 looks fine :smile:
 

Related to How Far Does the Ball Travel Horizontally Before Bouncing?

1. How do you calculate horizontal distance?

The horizontal distance can be calculated by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the horizontal distance would be the length of one of the sides, while the other side represents the vertical distance. By solving for the hypotenuse, you can determine the horizontal distance.

2. What is the importance of finding horizontal distance?

Finding horizontal distance is important in various fields such as engineering, surveying, and physics. It helps in determining the distance between two points on a horizontal plane, which is necessary for creating accurate maps, designing structures, and calculating projectile motion, among others.

3. How do you measure horizontal distance?

Horizontal distance can be measured using a variety of tools, such as a tape measure, a rangefinder, or a theodolite. These tools use different methods, such as direct measurement or triangulation, to determine the distance between two points on a horizontal plane.

4. What are some factors that can affect horizontal distance?

Some factors that can affect horizontal distance include the elevation of the starting and ending points, the curvature of the Earth, and obstacles in the path. These factors may need to be taken into account when calculating or measuring horizontal distance to ensure accuracy.

5. Can horizontal distance be negative?

No, horizontal distance cannot be negative. It is a measure of the length of a horizontal line between two points and, therefore, can only have positive values. However, if the direction of the line is taken into account, it can be described as either positive or negative, depending on the direction it is measured in.

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