anonymous
  • anonymous
hey guys, i need some help with projectile motion. i got 2/3 but i need help for the last one
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
A ball is thrown horizontally at 19 m/s from a clifftop 55 m above the sea level. Find: a) the time to land; 3.350296971 b) the angle at which it hits the water; 58.77 c) the speed at which it hits the water??
anonymous
  • anonymous
Use conservation of energy, it is the easies approach. We know from the assumptions associated with projectile motion that \(v_x = {\rm constant}\). We can find the velocity gained in the y-direction from conservation of energy, as\[{1 \over 2} m v_y^2 = mgh \rightarrow {1 \over 2} v_y^2 = gh \rightarrow v_y^2 = 2gh\] Then the magnitude of both velocity vectors can be found as\[v = \sqrt{v_x^2 + v_y^2}\]
anonymous
  • anonymous
ya but i had found 11.52 for the y and 19 for the x since it is the same. when you do that you will get around 22.2 and that answer was wrong when i submitted it :S

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anonymous
  • anonymous
Double check you \(v_y\). I'm getting \(v \approx 38\) from the magnitude.
anonymous
  • anonymous
but how? cuz i had used those numbers to get my angle
anonymous
  • anonymous
It's simple math. \[v_y = \sqrt{2 \cdot 9.81 \cdot 55} \approx 33\] Therefore, \[v = \sqrt{19^2 + (2 \cdot 9.81 \cdot 55)} \approx 38\] The angle is found as\[\tan \theta = {v_y \over v_x}\]
anonymous
  • anonymous
so the angle is 60?
anonymous
  • anonymous
Yes.
anonymous
  • anonymous
odd how it accepted my answer of 58.77 lol thanks a lot though :) care to help me with a similar one?
anonymous
  • anonymous
It probably is programmed to allow for a certain amount of % error. 58.77 is less than 3% different than 60.
anonymous
  • anonymous
Did it take 38 as the speed?
anonymous
  • anonymous
yes :)
anonymous
  • anonymous
Sure. Post it up and I'll take a look at it.
anonymous
  • anonymous
Great!
anonymous
  • anonymous
is there another way of solving for it without energy? like using kinematics?
anonymous
  • anonymous
OMG I REALISED MY STUPID MISTAKE. you can use kinematics to solve for vf but that vf will b for the y so then you have to do it for the total!
anonymous
  • anonymous
so stupid :P sry its because i wrote everywhere LOL quiet a big mess :P
anonymous
  • anonymous
Absolutely. \[v_y^2 = 2ad\], which is derived from constant acceleration kinematics. Notice, its the same equation we got when we used energy.
anonymous
  • anonymous
Indeed. The gravitational acceleration only acts in the vertical direction.
anonymous
  • anonymous
Take the time to work through problems in a very organized manner. It's a pain, I know, and uses a ton of paper, but it will help you not silly mistakes like that. :)
anonymous
  • anonymous
ya true :P i was doing other ones from my friend and i made the dumbest mistake. like i expanded (x+1.1)^2 which became x^2+2.2x+1.21 and that was multiplied by 4.9 but i didnt multiply the last term. and i couldnt figure out why my answring was wrong :P Untill i checked my work LOL

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