Answer:
a) The speed of the slider is 4.28 in/s
b) The velocity vector is 2.33 in/s
Explanation:
a) According to the diagram 1 in the attached image:
Also:
![v_{C} =v_{A}+w_{AC}*r_{C/A}\\v_{Ci}=-3j+\left[\begin{array}{ccc}i&j&k\\0&0&w_{AC} \\6.883&-9.829&0\end{array}\right]\\v_{Ci}=-3j+(0+9.829w_{AC} i-(0-6.883w_{AC})j\\v_{Ci}=9.829w_{AC}i+(-3+6.883w_{AC})j](https://tex.z-dn.net/?f=v_%7BC%7D%20%3Dv_%7BA%7D%2Bw_%7BAC%7D%2Ar_%7BC%2FA%7D%5C%5Cv_%7BCi%7D%3D-3j%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C0%260%26w_%7BAC%7D%20%5C%5C6.883%26-9.829%260%5Cend%7Barray%7D%5Cright%5D%5C%5Cv_%7BCi%7D%3D-3j%2B%280%2B9.829w_%7BAC%7D%20i-%280-6.883w_%7BAC%7D%29j%5C%5Cv_%7BCi%7D%3D9.829w_%7BAC%7Di%2B%28-3%2B6.883w_%7BAC%7D%29j)
If we comparing both sides of the expression:
b) According to the diagram 2 in the attached image:
![v_{C}=v_{A}+w_{AC}r_{C/A}\\v_{C}=-3j+\left[\begin{array}{ccc}i&j&k\\0&0&w_{AC}\\7.713&-9.192&0\end{array}\right] \\v_{Ci}=-3j+(9.192w_{AC})i+7.713w_{AC}j\\v_{Ci}=9.192w_{AC}i+(7.713w_{AC}-3)j](https://tex.z-dn.net/?f=v_%7BC%7D%3Dv_%7BA%7D%2Bw_%7BAC%7Dr_%7BC%2FA%7D%5C%5Cv_%7BC%7D%3D-3j%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C0%260%26w_%7BAC%7D%5C%5C7.713%26-9.192%260%5Cend%7Barray%7D%5Cright%5D%20%5C%5Cv_%7BCi%7D%3D-3j%2B%289.192w_%7BAC%7D%29i%2B7.713w_%7BAC%7Dj%5C%5Cv_%7BCi%7D%3D9.192w_%7BAC%7Di%2B%287.713w_%7BAC%7D-3%29j)
Comparing both sides of the expression:
![v_{B}=v_{C}+w_{AC}r_{B/C}\\v_{B}=3.57i+\left[\begin{array}{ccc}i&j&k\\0&0&0.388\\-3.856&4.59&0\end{array}\right] \\v_{B}=3.57i+(0-1.78)i-(0+1.499)j\\v_{B}=1.787i-1.499j\\|v_{B}|=\sqrt{1.787^{2}+1.499^{2} } =2.33in/s](https://tex.z-dn.net/?f=v_%7BB%7D%3Dv_%7BC%7D%2Bw_%7BAC%7Dr_%7BB%2FC%7D%5C%5Cv_%7BB%7D%3D3.57i%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C0%260%260.388%5C%5C-3.856%264.59%260%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5Cv_%7BB%7D%3D3.57i%2B%280-1.78%29i-%280%2B1.499%29j%5C%5Cv_%7BB%7D%3D1.787i-1.499j%5C%5C%7Cv_%7BB%7D%7C%3D%5Csqrt%7B1.787%5E%7B2%7D%2B1.499%5E%7B2%7D%20%20%7D%20%3D2.33in%2Fs)
Explanation:
(a)
The initial vertical velocity is 13 m/s. At the maximum height, the vertical velocity is 0 m/s.
v = at + v₀
0 = (-9.8) t + 13
t ≈ 1.33 s
(b)
Immediately prior to the explosion, the ball is at the maximum height. Here, the vertical velocity is 0 m/s, and the horizontal velocity is constant at 25 m/s.
v = √(vx² + vy²)
v = √(25² + 0²)
v = 25 m/s
(c)
Momentum is conserved before and after the explosion.
In the x direction:
m vx = ma vax + mb vbx
m (25) = (⅓ m) (0) + (⅔ m) (vbx)
25m = (⅔ m) (vbx)
25 = ⅔ vbx
vbx = 37.5 m/s
And in the y direction:
m vy = ma vay + mb vby
m (0) = (⅓ m) (0) + (⅔ m) (vby)
0 = (⅔ m) (vby)
vby = 0 m/s
Since the vertical velocity hasn't changed, and since Fragment B lands at the same height it was launched from, it will have a vertical velocity equal in magnitude and opposite in direction as its initial velocity.
vy = -13 m/s
And the horizontal velocity will stay constant.
vx = 37.5 m/s
The velocity vector is (37.5 i - 13 j) m/s. The magnitude is:
v = √(vx² + vy²)
v = √(37.5² + (-13)²)
v ≈ 39.7 m/s
Answer:
There are many topics related to physics such as :
Kinematics
Dynamics
Light
Sound
A falling raindrop
Kinetic energy and potential energy are both applied when a body or object is falling.
<span>A spring is water coming from under the ground to the surface of the earth and a stream is water that is running along the ground through a trench like place on earth down a hill or steep a area.</span>
