Calculating Snowball Trajectories: Solving for Angle and Time

[dizco29]

Hey guys, have a few questions I was hoping you guys could help me out with.

*

4.13)******* One strategy in a snowball fight is to throw a snowball at a high angle over level ground. While your opponent is watching the first one, a second snowball is thrown at a low angle timed to arrive before or at the same time as the first one. Assume both snowballs are thrown at an angle of 70.0 degrees with respect to the horizontal. (a) at what angle should the second snowball be thrown to arrive at the same point as the first? (b) How many seconds later should the second snowball be thrown after the first to arrive at the same time?

What I did:

First I drew a digram and made a line represting the resultant (r) vector which is 25.00 m/s. I knew my angle, which is 70 degrees. from this, I'm able to use one of 4 formulas to find the components of r which = 25 degrees.

for velocity:
Vxi = (vi)(Cos)(angle)
Vyi = (vi)(Sin)(Angle) - gt

for displacement:
x = (vi)(Cos)(angle)(t)
y = (vi)(Sin)(angle)(t) - 1/2(g)t^2

so I solved the initial velocity for the x components, which was:
vxi=(25)(Cos)(70) = 8.5 m/s

and the y component

vyi= (25)(sin)(70) = 23.49 m/s

at this point, I tried a formula for the x component for displacement, and got:

8.5t

but I figured I could find time by using the y component seeing as how I know the snowball will be at 0 velocity at the max height. So I could use the kinematic equation vf = vi+at . so if I plug that in I get:

0 = 23.46 + (-9.8)t

-23.46/-9.8 = 2.3969 s

and I would have to x2 so that it covers the whole distance so the t = 4.793 s

now, if I plug that into the equation 8.5t , I would get :

8.5 (4.793) = 40.7405m

So now I know my displacement of snowball 1 (and I'm assuming for snowball 2)

Now at this point I'm stuck. I don't know what to do with the information I have to get the missing angle for snowball 2 and have no idea how to calculate what I need to launch snowball 2 for it to = the time for snowball one. Can anyone help?

I also had a comment about how the first question didn't make sense. I double-checked the question and it was exactly the way I stated above. I'm also going to do 3 posts as someone said it was confusing having all 3 in one post. Thanks

 

[Noein]

The two angles that will reach the same horizontal range are complementary, meaning that they add up to 90 degrees.

 

[dizco29]

oooh! So what you're saying is that my missing angle is 20 degrees for the second snowball? Is it really that easy? lol.

 

[dizco29]

Oh Dan! You were absolutley right! I made a typo with the question. here's the question again but with the correction underlined. I must have missed it when I re-read the question!

4.13)******* One strategy in a snowball fight is to throw a snowball at a high angle over level ground. While your opponent is watching the first one, a second snowball is thrown at a low angle timed to arrive before or at the same time as the first one. Assume both snowballs are thrown with a speed of 25.0 m/s. The first one is thrown at an angle of 70.0 degrees with respect to the horizontal. (a) at what angle should the second snowball be thrown to arrive at the same point as the first? (b) How many seconds later should the second snowball be thrown after the first to arrive at the same time?

 

[Locrian]

My students love the complementary argument because it saves them all the trouble of solving the problem. However, if you cannot make an excellent case to yourself on why that should be true, you shouldn't use it! Otherwise you may find yourself on a test facing a problem where you aren't sure if you can use it or not.

This problem is not tricky, but it does take a while to set up. Break everything into components and you'll end up with four sets of information - two for the first snowball (x & y), and two for the second. While you may be able to arrive at this solution quickly, don't always look for the easy way out. Take the time to solve for many of the variables, and as the puzzle pieces come into place you should eventually come to the variable you are being asked to solve.

 

[dizco29]

k, I think I solved this one. I don't want to bother writing all my steps. I just want to check the answer. If it's wrong, don't tell me the answer, I'll post up the work if the answers are wrong.

So for a) it's 20 degrees (Because complemntary angles with the same intital speed arrive at the same displacement.

b)The second snowball will have to be thrown 3.06 seconds after the first one to arrive at the same time.



If it's wrong, I'll type out the steps

thnaks again!