Projectile motion ball question

In summary, the ratio of distances x1/x2 can be determined by the ratio of times t1/t2 which is equal to the square root of 2, given that the higher ball falls twice the distance of the lower ball.
  • #1
Kristin_Z
9
0
A ball moving with speed v rolls off a shelf of height h and strikes the floor below a distance x1 from the edge. A second ball moving with the same speed rolls of a self of height 2h and strikes the floor a distance x2 away from the edge. Determine the ratio of distances x1/x2.
[tex]\Delta[/tex]x=Vxt
[tex]\Delta[/tex]y=vt +1/2st2
The horizontal motion of the ball is constant and, therefore, not affected by the height from which it rolls. But I cannot figure out how to formulate the ratio of the distances. I know that time relates the two equations of motion and that because the ball is rolling it has no initial vertical velocity and that since it is free fall the acceleration would be the same for the two equations. I just can't seem to get the equation to make sense when I write it out. Any help would be greatly appreciated. Thanks!
 
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  • #2
Kristin_Z said:
A ball moving with speed v rolls off a shelf of height h and strikes the floor below a distance x1 from the edge. A second ball moving with the same speed rolls of a self of height 2h and strikes the floor a distance x2 away from the edge. Determine the ratio of distances x1/x2. The horizontal motion of the ball is constant and, therefore, not affected by the height from which it rolls. But I cannot figure out how to formulate the ratio of the distances. I know that time relates the two equations of motion and that because the ball is rolling it has no initial vertical velocity and that since it is free fall the acceleration would be the same for the two equations. I just can't seem to get the equation to make sense when I write it out. Any help would be greatly appreciated. Thanks!

Well I can see you are almost grasping it.

The horizontal motion is constant, that's true, but what affects the distance at which it lands?

d1 = V*t1
d2 = V*t2

So ... the ratio of the distances then will be in the same ratio as the ratio of the times won't it?

And now is there some way to relate the ratio of the times using the heights?
 
  • #3
I think I have it now.

2y = 1/2 at12 divided by y = 1/2 at22

gives me 2= t12t22

so t1t2 =square root of 1/2.

Thanks for your help, still not entirely sure I understand what I did. I guess that's what practice is for.
 
  • #4
Kristin_Z said:
I think I have it now.

so t1t2 =square root of 1/2.
.

Check this step.
 
  • #5
Kristin_Z said:
I think I have it now.

2y = 1/2 at12 divided by y = 1/2 at22

gives me 2= t12t22

so t1t2 =square root of 1/2.

Thanks for your help, still not entirely sure I understand what I did. I guess that's what practice is for.

I think you really meant
2= t12/t22

Which yields the ratio

t1/t2 = √2

But I would note the original statement has y2 being 2*y1, so I think you have your subscripts reversed.

The higher ball would fall farther from the base by a factor of √2 is the sense of you should be grasping.
 

What is projectile motion?

Projectile motion refers to the motion of an object that is moving through the air or any other medium under the influence of gravity, with only the force of gravity acting on it.

What factors affect the trajectory of a projectile?

The trajectory of a projectile is affected by its initial velocity, angle of launch, air resistance, and the force of gravity.

How can the range of a projectile be calculated?

The range of a projectile can be calculated using the formula: R = (v2sin(2θ))/g, where R is the range, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

What is the maximum height reached by a projectile?

The maximum height reached by a projectile can be calculated using the formula: H = (v2sin2(θ))/2g, where H is the maximum height reached, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

What are some real-life applications of projectile motion?

Some real-life applications of projectile motion include throwing a ball, launching a rocket, and shooting a projectile from a gun or bow. It is also used in sports such as basketball, baseball, and golf.

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