Answer:
In words, it could be said that the force times the time equals the mass times the change in velocity. In physics, the quantity Force • time is known as impulse. And since the quantity m•v is the momentum, the quantity m•Δv must be the change in momentum. The equation really says that the Impulse = Change in momentum.
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Answer:
ms⁻¹
Explanation:
= diameter of merry-go-round = 4 m
= radius of merry-go-round =
=
= 2 m
= moment of inertia = 500 kgm²
= angular velocity of merry-go-round before ryan jumps = 2.0 rad/s
= angular velocity of merry-go-round after ryan jumps = 0 rad/s
= velocity of ryan before jumping onto the merry-go-round
= mass of ryan = 70 kg
Using conservation of angular momentum
![Iw_{i} - m v r = (I + mr^{2})w_{f}](https://tex.z-dn.net/?f=Iw_%7Bi%7D%20-%20m%20v%20r%20%3D%20%28I%20%2B%20mr%5E%7B2%7D%29w_%7Bf%7D)
![(500)(2.0) - (70) v (2) = (I + mr^{2})(0)](https://tex.z-dn.net/?f=%28500%29%282.0%29%20-%20%2870%29%20v%20%282%29%20%3D%20%28I%20%2B%20mr%5E%7B2%7D%29%280%29)
![1000 = 140 v](https://tex.z-dn.net/?f=1000%20%3D%20140%20v)
ms⁻¹
Answer:
1.97 seconds
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.8 m/s²
![s=ut+\frac{1}{2}at^2\\\Rightarrow 21=4.5t+\frac{1}{2}\times -9.8\times t^2\\\Rightarrow 21=-4.5t-4.9t^2\\\Rightarrow 4.9t^2+4.5t-28=0\\\Rightarrow 49t^2+45t-280=0](https://tex.z-dn.net/?f=s%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2%5C%5C%5CRightarrow%2021%3D4.5t%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20-9.8%5Ctimes%20t%5E2%5C%5C%5CRightarrow%2021%3D-4.5t-4.9t%5E2%5C%5C%5CRightarrow%204.9t%5E2%2B4.5t-28%3D0%5C%5C%5CRightarrow%2049t%5E2%2B45t-280%3D0)
Solving the above equation we get
![t=\frac{-45+\sqrt{45^2-4\cdot \:49\left(-280\right)}}{2\cdot \:49}, \frac{-45-\sqrt{45^2-4\cdot \:49\left(-280\right)}}{2\cdot \:49}\\\Rightarrow t=1.97, -2.89](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-45%2B%5Csqrt%7B45%5E2-4%5Ccdot%20%5C%3A49%5Cleft%28-280%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A49%7D%2C%20%5Cfrac%7B-45-%5Csqrt%7B45%5E2-4%5Ccdot%20%5C%3A49%5Cleft%28-280%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A49%7D%5C%5C%5CRightarrow%20t%3D1.97%2C%20-2.89)
So, the time the package was in the air is 1.97 seconds