Calculating a ratio in Free Fall motion

[vAhmed]

Homework Statement

A ball is thrown upward with a speed v 1. The ball reaches a maximum height of y=h. What is the ratio of the speed of the ball,v 2 , at y=h/2, to the initial upward speed of the ball,v 1 , at y=0?

Homework Equations

I attached a picture.

We are currently studying the four equations for motions in a straight line.

The Attempt at a Solution

I know that the acceleration would be constant as a = -g = -9.81m/s^2. And as the ball moves upward the acceleration will slow down the ball due to gravity. The ball was thrown meaning that v1≠ 0. So I set v1 = 9.81 m/s, and v2 = 9.81/2 = 4.9 m/s. Then V2/V1 equals 4.9/9.8 = 0.50. Although I think it doesn't make sense to divide 9.81 by 2. At this point, I couldn't do any better.

 

[jbriggs444]

I tried to calculate the velocity at y=0 to divide it by the velocity at y=h/2 but couldn't do it. I also thought of substituting or using imaginary values.

You seen to have removed the template where you were asked to show your work and show applicable equations.

We cannot tell what you have tried unless you tell us.

 

[vAhmed]

You seen to have removed the template where you were asked to show your work and show applicable equations.

We cannot tell what you have tried unless you tell us.

Sorry for that, I posted another thread.

 

[jbriggs444]

I tried to calculate the velocity at y = 0 and y = h/2 but I couldn't. I also thought about substituting imaginary values.

It's not just the template you need. You need to show your work. Tell us what things you have tried. Not just the fact that they've failed.

 

[vAhmed]

Homework Statement

A ball is thrown upward with a speed v 1. The ball reaches a maximum height of y=h. What is the ratio of the speed of the ball,v 2 , at y=h/2, to the initial upward speed of the ball,v 1 , at y=0?

Homework Equations

I attached a picture.
View attachment 231564
We are currently studying the four equations for motions in a straight line.

The Attempt at a Solution

I know that the acceleration would be constant as a = -g = -9.81m/s^2. And as the ball moves upward the acceleration will slow down the ball due to gravity. The ball was thrown meaning that v1≠ 0. So I set v1 = 9.81 m/s, and v2 = 9.81/2 = 4.9 m/s. Then V2/V1 equals 4.9/9.8 = 0.50. Although I think it doesn't make sense to divide 9.81 by 2. At this point, I couldn't do any better.

I don't want the answer, I just want to know what should I do to solve it.

 

[vAhmed]

It's not just the template you need. You need to show your work. Tell us what things you have tried. Not just the fact that they've failed.

I got the answer (b) but I'm not certain about it.

 

[kuruman]

The work that you have shown in post #1 assumes that the initial speed is 9.81 m/s. You may not assume that. All you know is that the initial speed is v₁. You also assume that the ball will have half the speed in half the height. That is simply wrong. The speed will have half its value in half the time required to reach height h, not in the time required to reach half the height. You have correctly divined that dividing by two makes no sense.

You are given two pairs of positions and speeds and you know of course that the acceleration is g down. Is there an equation among the ones that you listed that relates displacement and speed and includes the acceleration? If so, use it to express with equations what the problem is telling you that is going on.

 

[CWatters]

Equation (v) relates the velocity to distance (height). However note that its an equation for V_y² not V_y so do you think it likely it will be going half the speed at half the height?

The first thing to do when asked for a ratio is to set up the division. What is the numerator an denominator in the case? The find equations for each and finally see if it can be simplified. Dies anything cancel?