Calculating the Catch: Solving for the Height of a Daredevil's Net

[Jameson]

Somebody please! help me

I have already posted this question but no one has given me any help. I need this answer, it is due soon.

A daredevil is shot out of a cannon at 24.0° to the horizontal with an initial speed of 26.0 m/s. A net is positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil?

I know how to set it up... I think

Vx= Vcos(theta)
Vy=Vsin(theta)

x = Vxt
t = x/Vx

y = Vyt + .5gt^2

HELP ME

 

[donjennix]

Nope -

y = Vyt - .5gt^2

Vy and g are in opposite directions

So you know t and you know how high the daredevil is at t

 

[Jameson]

When I do that I get 43.97... which is wrong. Can you tell me what I've done wrong?

 

[z-component]

If you are using y = Vyt - .5gt^2 make sure you are using 9.80 m/s^2 for g. The minus sign accounts for what some textbooks give for gravity, 9.80 m/s^2. Only use y = Vyt + .5gt^2 when you are using -9.80 m/s^2 for gravity. Be sure not to mix them up.

z-component

 

[HawKMX2004]

I was taught Vertical components have nothing to do with horizontal components, so here is how i would solve it.

A daredevil is shot out of a cannon at 24.0° to the horizontal with an initial speed of 26.0 m/s. A net is positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil?

Start with a freebody diagram and then solve for time in the X-Direction

Xf = Xi +ViT + .5gT^2
T^2 = Xf - ViT / .5g
T^3 = Xf - Vi / .5g
T^3 = 50 - 26 / .5(9.8)
T^3 = 24 / 4.9
T^3 = 4.9
T = 1.7 seconds <--- Remember this

Yf = Yi +ViT +.5gT^2 G is going to equal sin(24)9.8 due to the angle launched

Yf = ViT + .5(cos(24)(9.8))T^2
Yf = (26)(1.7) + .5(cos(24)(9.8))(1.7^2)
Yf = 44.2 + 12.9
Yf = 57.1 m above the end of the cannon barrel

I'm not positive if that is correct or not, but it sounds reasonable to me

I hope that helped you understand the 2D motion

 

[donjennix]

When I do that I get 43.97... which is wrong. Can you tell me what I've done wrong?

Well you added instead of subtracting. I get the surprising answer of 0.547 meter from the floor -- I would have thought it was going to be higher.

{Vyt = 10.58*2.11 = 22.26 ; .5*g*t^2= 4.9*2.11*2.11 = 21.71. If you add instead of subtract you get your answer.}

 

[HawKMX2004]

wow, those are 3 very different answers...can you explain how you got .57 meters? Because i may have showed him wrong

 

[Zlex]

I don't know how you guys got either of those answers

I got 43.8

 

[Zlex]

I was taught Vertical components have nothing to do with horizontal components, so here is how i would solve it.

A daredevil is shot out of a cannon at 24.0° to the horizontal with an initial speed of 26.0 m/s. A net is positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil?

Start with a freebody diagram and then solve for time in the X-Direction

Xf = Xi +ViT + .5gT^2

Uhh!

Xf = Xi +ViT + .5aT^2

Assume no AR, a = 0, not 9.8

 

[Jameson]

I've gotten the 43.97 answer and the really small one, depending on whether you subtract or add the second part. Someone please help. It's due tomorrow!

 

[HawKMX2004]

oh..no wonder i messed up..im not sure ill have to re-work this one

 

[Zlex]

Alright, I will explain how I did it.

HORIZONTAL COMPONENT

$$dD = 50 m$$
$$v_o = 24cos(30) m/s$$
$$v_f = ?$$
$$dT = ?$$
$$a = 0 m/s^2$$

We don't care about $$v_f$$.

Solving for $$dT$$:

$$dD = v_i*dT+0.5*a*dT$$
$$50 = 26cos(24)*dT$$
$$dT = 2.1 s$$


VERTICAL COMPONENT

$$dD = ?$$
$$v_i = 26sin(24) m/s$$
$$v_f = ?$$
$$dT = 2.1 s$$
$$a = -9.8 m/s^2$$

Solving for dD

$$dD = v_i*dT + 0.5*a*dT^2$$
$$dD = 26sin24*2.1+0.5*-9.8*2.1^2$$

$$dD = 0.598$$

 

[HawKMX2004]

is there a website your doing all that on? or how do you get that font type/style

 

[cdhotfire]

is it me going crazy or is this a double post?

 

[Jameson]

Has anyone else used LON-CAPA for homework before? I'm getting the exact same answers you guys are, but it says I'm wrong.

 

[cdhotfire]

Im sorry but what is this LON-CAPA?

 

[donjennix]

How high iis the cannon above the ground? Is that stated in the problem? If the height is H then the answer that many are getting should be incremented by H. The basic Newtonian setup has to be right.

 

[Parth Dave]

it probably has something to do with rounding. Because if you round the time to 2.1 seconds you get .598 m, but if you don't round it at all you get 0.548. Either way, the process is right, so play around with rounding.