Answer:
The acceleration of the wallet is ![3\hat{i}+6\hat{j}](https://tex.z-dn.net/?f=3%5Chat%7Bi%7D%2B6%5Chat%7Bj%7D)
Explanation:
Given that,
Radius of purse r= 2.30 m
Radius of wallet r'= 3.45 m
Acceleration of the purse ![a=2\hat{i}+4.00\hat{j}](https://tex.z-dn.net/?f=a%3D2%5Chat%7Bi%7D%2B4.00%5Chat%7Bj%7D)
We need to calculate the acceleration of the wallet
Using formula of acceleration
![a=r\omega^2](https://tex.z-dn.net/?f=a%3Dr%5Comega%5E2)
Both the purse and wallet have same angular velocity
![\omega=\omega'](https://tex.z-dn.net/?f=%5Comega%3D%5Comega%27)
![\sqrt{\dfrac{a}{r}}=\sqrt{\dfrac{a'}{r'}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cdfrac%7Ba%7D%7Br%7D%7D%3D%5Csqrt%7B%5Cdfrac%7Ba%27%7D%7Br%27%7D%7D)
![\dfrac{a}{r}=\dfrac{a'}{r'}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%7D%7Br%7D%3D%5Cdfrac%7Ba%27%7D%7Br%27%7D)
![\dfrac{a'}{a}=\dfrac{r'}{r}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%27%7D%7Ba%7D%3D%5Cdfrac%7Br%27%7D%7Br%7D)
![\dfrac{a'}{a}=\dfrac{3.45}{2.30}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%27%7D%7Ba%7D%3D%5Cdfrac%7B3.45%7D%7B2.30%7D)
![\dfrac{a'}{a}=\dfrac{3}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%27%7D%7Ba%7D%3D%5Cdfrac%7B3%7D%7B2%7D)
![a'=\dfrac{3}{2}\times(2\hat{i}+4.00\hat{j})](https://tex.z-dn.net/?f=a%27%3D%5Cdfrac%7B3%7D%7B2%7D%5Ctimes%282%5Chat%7Bi%7D%2B4.00%5Chat%7Bj%7D%29)
![a'=3\hat{i}+6\hat{j}](https://tex.z-dn.net/?f=a%27%3D3%5Chat%7Bi%7D%2B6%5Chat%7Bj%7D)
Hence, The acceleration of the wallet is ![3\hat{i}+6\hat{j}](https://tex.z-dn.net/?f=3%5Chat%7Bi%7D%2B6%5Chat%7Bj%7D)
<span>You should deflect the
ball in order to maximize your speed on the skateboard.
Since this creates a larger impulse, you want to deflect the ball. Splitting it
up into catching and throwing the ball may by something you can think of deflecting
the ball. First, you need to catch the ball, which in turn would push you
forward with some speed. (The speed we are talking about should obviously be
equal to option A, where you catch the ball). Now, throw the ball back to him
since these two processes are equal to deflecting the ball. Throwing a mass away
from you would cause or enable you to move even fast.</span>
Answer:
meters
Explanation:The question ask for the maximum value of the function f(t) which can be find by find the maxima of the function
The maxima of the function occurs when the slope is zero. i.e.
![\frac{df}{dt} =0\\\frac{df}{dt} =\frac{d}{dt} (-4.9t^2+16t+2)\\\frac{df}{dt} =-4.9*2t+16\\-9.8t+16=0\\t=16/9.8\\t=1.63 secs](https://tex.z-dn.net/?f=%5Cfrac%7Bdf%7D%7Bdt%7D%20%3D0%5C%5C%5Cfrac%7Bdf%7D%7Bdt%7D%20%3D%5Cfrac%7Bd%7D%7Bdt%7D%20%28-4.9t%5E2%2B16t%2B2%29%5C%5C%5Cfrac%7Bdf%7D%7Bdt%7D%20%3D-4.9%2A2t%2B16%5C%5C-9.8t%2B16%3D0%5C%5Ct%3D16%2F9.8%5C%5Ct%3D1.63%20secs)
Hence the maxima occurs at t=1.63 seconds
The maximum value of f is
![f(1.63)=-4.9(1.63^2)+16(1.63)+2\\f(1.63)=15.06\\](https://tex.z-dn.net/?f=f%281.63%29%3D-4.9%281.63%5E2%29%2B16%281.63%29%2B2%5C%5Cf%281.63%29%3D15.06%5C%5C)
hence maximum height is found to be
meters
OD because Boyle’s law specifically states
Given:
Area of pool = 3m×4m
Diameter of orifice = 0.076m
Outlet Velocity = 6.3m/s
Accumulation velocity = 1.5cm/min
Required:
Inlet flowrate
Solution:
The problem can be solved by this general formula.
Accumulation = Inlet flowrate - Outlet flowrate
Accumulation velocity × Area of pool = Inlet flowrate - Outlet velocity × Area of orifice
First, we need to convert the units of the accumulation velocity into m/s to be consistent.
Accumulation velocity = 1.5cm/min × (1min/60s)×(1m/100cm)
Accumulation velocity = 0.00025 m/s
We then calculate the area of the pool and the area of the orifice by:
Area of pool = 3 × 4 m²
Area of pool = 12m²
Area of orifice = πd²/4 = π(0.076m)²/4
Area of orifice = 0.00454m²
Since we have all we need, we plug in the values to the general equation earlier
Accumulation velocity × Area of pool = Inlet flowrate - Outlet velocity × Area of orifice
0.00025 m/s × 12m² = Inlet flowrate - 6.3m/s × 0.00454m²
Transposing terms,
Inlet flowrate = 0.316 m³/s