Determining the height an arrow reaches when shot from a bow

[otownsend]

Hi,

I'm trying to attempt the "Try it yourself" on the bottom-right corner of the image attached, but I am struggling.

As you see in the other image I attached, in one scenario I took into account the kinetic friction (which did not lead me anywhere since I needed to know the velocity of the arrow once in the air), and then in another scenario I did not take it into account (which led me to the wrong answer of about 81 meters). The actual answer is 28 meters.

I hope someone can help me solve this question!:/

 

[tnich]

Hi,

I'm trying to attempt the "Try it yourself" on the bottom-right corner of the image attached, but I am struggling.

As you see in the other image I attached, in one scenario I took into account the kinetic friction (which did not lead me anywhere since I needed to know the velocity of the arrow once in the air), and then in another scenario I did not take it into account (which led me to the wrong answer of about 81 meters). The actual answer is 28 meters.

I hope someone can help me solve this question!:/

View attachment 233862
View attachment 233863

Actually, in the problem statement, the answer is printed upside down. Take another look at it. You interpreted it as 28m, but it is actually 82m.

 

[A.T.]

the answer is printed upside down.

Amazing that this apparently worked here!

 

[gneill]

The height achieved should actually be just a tad less than what they gave since they failed to take into account the distance the arrow rose while being accelerated by the bow.

 

[haruspex]

The height achieved should actually be just a tad less than what they gave since they failed to take into account the distance the arrow rose while being accelerated by the bow.

Doesn't that cancel out? Yes, it made the launch speed a little less but that matches the contribution made to the eventual height. Essentially, initial stored energy equals GPE achieved.

 

[gneill]

Doesn't that cancel out? Yes, it made the launch speed a little less but that matches the contribution made to the eventual height. Essentially, initial stored energy equals GPE achieved.

I suppose, If you count the distance of the bow stretch as part of the height achieved. I was thinking that the height desired was the height achieved by the projectile after launch.

 

[otownsend]

Oh wow -_______- sorry about not turning my head properly side-ways... I'll be more careful next time before I make a post.

 

[gneill]

Oh wow -_______- sorry about not turning my head properly side-ways... I'll be more careful next time before I make a post.

Hah!. Sideways wouldn't do in this case. Completely upside down is the necessary contortion.