Answer:
Time = 0.55 s
Height = 8.3 m
Explanation:
The ball is dropped and therefore has an initial velocity of 0. Its acceleration, g, is directed downward in the same direction as its displacement,
.
The dart is thrown up in which case acceleration, g, acts downward in an opposite direction to its displacement,
. Both collide after travelling for a time period, t. Let the height of the dart from the ground at collision be
and the distance travelled by the ball measured from the top be
.
It follows that
.
Applying the equation of motion to each body (h = v_0t + 0.5at^2),
Ball:
(since
.)
![h_b=4.9t^2](https://tex.z-dn.net/?f=h_b%3D4.9t%5E2)
Dart:
(the acceleration is opposite to the displacement, hence the negative sign)
![h_d=17.8\times t - 4.9t^2](https://tex.z-dn.net/?f=h_d%3D17.8%5Ctimes%20t%20-%204.9t%5E2)
But
![h_b+h_d =9.8](https://tex.z-dn.net/?f=h_b%2Bh_d%20%3D9.8)
![17.8\times t - 4.9t^2+4.9t^2 =9.8](https://tex.z-dn.net/?f=17.8%5Ctimes%20t%20-%204.9t%5E2%2B4.9t%5E2%20%3D9.8)
![17.8\times t = 9.8](https://tex.z-dn.net/?f=17.8%5Ctimes%20t%20%3D%209.8)
![t = 0.55](https://tex.z-dn.net/?f=t%20%3D%200.55)
The height of the collision is the height of the dart above the ground,
.
![h_d=17.8\times t - 4.9t^2](https://tex.z-dn.net/?f=h_d%3D17.8%5Ctimes%20t%20-%204.9t%5E2)
![h_d=17.8\times 0.55 - 4.9\times(0.55)^2](https://tex.z-dn.net/?f=h_d%3D17.8%5Ctimes%200.55%20-%204.9%5Ctimes%280.55%29%5E2)
![h_d=9.79 - 1.48225](https://tex.z-dn.net/?f=h_d%3D9.79%20-%201.48225)
![h_d=8.3](https://tex.z-dn.net/?f=h_d%3D8.3)
You have to put the work to it and but the answer is 30cm
Answer:
Explanation:
check attached image for figure, there is supposed to be a figure for this question containing a distance(height of collar at position A) but i will assume 0.2m or 200mm
Consider the energy equilibrium of the system
![U_{A-B}=\bigtriangleup T\\\\F\cos 30°\times h_A - F\sin30°\times h_A + Wh_A=\frac{1}{2}m(v^2_B-v^2_A)\\\\v_B=\sqrt{\frac{2Fh_A(\cos 30° - \sin30°)+mgh_A}{m+v^2_A}}](https://tex.z-dn.net/?f=U_%7BA-B%7D%3D%5Cbigtriangleup%20T%5C%5C%5C%5CF%5Ccos%2030%C2%B0%5Ctimes%20h_A%20-%20F%5Csin30%C2%B0%5Ctimes%20h_A%20%2B%20Wh_A%3D%5Cfrac%7B1%7D%7B2%7Dm%28v%5E2_B-v%5E2_A%29%5C%5C%5C%5Cv_B%3D%5Csqrt%7B%5Cfrac%7B2Fh_A%28%5Ccos%2030%C2%B0%20-%20%5Csin30%C2%B0%29%2Bmgh_A%7D%7Bm%2Bv%5E2_A%7D%7D)
Here, F is the force acting on the collar,
is the height of the collar at position A, m is the mass of the collar C, g is the acceleration due to gravity,
is the velocity of the collar at position B, and
is the velocity of the collar at A
Substitute 14.4N for F, 0.2m for
, 1.5kg for m,
for g and 0 for ![v_A](https://tex.z-dn.net/?f=v_A)
![v_B=\sqrt{\frac{2(14.4\times 0.2(\cos 30° - \sin30°)+1.5\times 9.81\times 0.2}{1.5+0}}\\\\=\sqrt{\frac{6.618}{1.5}}\\\\=4.412m/s](https://tex.z-dn.net/?f=v_B%3D%5Csqrt%7B%5Cfrac%7B2%2814.4%5Ctimes%200.2%28%5Ccos%2030%C2%B0%20-%20%5Csin30%C2%B0%29%2B1.5%5Ctimes%209.81%5Ctimes%200.2%7D%7B1.5%2B0%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%5Cfrac%7B6.618%7D%7B1.5%7D%7D%5C%5C%5C%5C%3D4.412m%2Fs)
Therefore, the velocity at which the collar strikes the end B is 4.412m/s
Question: I was honored to be a part of an online group of students from the United States, Africa, and China seeking solutions to water shortages. While we all had great enthusiasm about changing the world, the project quickly dissolved because no one was willing to listen to differing viewpoints.
Which line could be added to show the difference a digital leader can make?
Answer:
The line that can be added to show the difference a digital leader can make is, "We saved the project by allowing each group to share their thoughts and then chose the best solutions"
Explanation:
A digital leader is the one who is innovative, creative, collaborative, experimental, curious and also able to network. The person should have forward thinking capability, most importantly should remain very adaptive, so that can remain relevant to the change. To archive this, he alone can do this. Must have different group of people through which could extract different ideas and views from which he/she could chose the right one for the desired situation.