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olya-2409 [2.1K]
3 years ago
15

20 points and brainliest!!!! Pls help er

Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
3 0
Slader could really help
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A 2.00 kg particle has the xy coordinates (−1.20 m, 0.500 m), and a 4.00 kg particle has the xy coordinates (0.600 m, −0.750 m).
Dafna11 [192]

Answer:

(x_{3},y_{3})=(-1.50\ m, -1.43\ m)

Step-by-step explanation:

Given:

Mass of the first particle m_{1} =2.0\ kg

Mass of the second particle m_{2} =4.0\ kg

Mass of the third particle m_{3} =\ ?

xy coordinate of the first particle (x_{1},y_{1})=(-1.20 m, 0.500 m)

xy coordinate of the second particle (x_{2},y_{2})=(0.600 m, -0.750 m)

coordinate of the centre of mass of three-particle system (x_{cm},y_{cm})=(-0.500 m, -0.700 m)

We need to find the xy coordinate of the third particle.

Solution:

First we calculate total mass of the three-particle system.

M = m_{1}+m_{2}+m_{3}

M = 2.0+4.0+3.0

M = 9.0\ kg

x coordinate of the centre of mass of the three-particle system are given as;

x_{cm}=\frac{1}{M}(m_{1}x_{1}+ m_{2}x_{2}+ m_{3}x_{3})

Rewrite the equation for x_{3}

m_{3}x_{3}=Mx_{cm}-m_{1}x_{1}-m_{2}x_{2}

Part a.

x_{3}=\frac{1}{m_{3}} (Mx_{cm}-m_{1}x_{1}-m_{2}x_{2})

Substitute all given values in above equation.

x_{3}=\frac{1}{3.0} (9.0\times (-0.5)-2.0\times (-1.20)-4.0\times (0.6))

x_{3}=-1.50\ m

Part b.

Similarly for y_{3} coordinate.

y_{3}=\frac{1}{m_{3}} (My_{cm}-m_{1}y_{1}-m_{2}y_{2})

Substitute all given values in above equation.

y_{3}=\frac{1}{3.0} (9.0\times (-0.7)-2.0\times 0.5-4.0\times (-0.75))

y_{3}=-1.43\ m

Therefore, xy coordinate of the third particle (x_{3},y_{3})=(-1.50\ m, -1.43\ m)

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Find the derivative r '(t) of the vector function r(t). t sin 6t , t2, t cos 7t Part 1 of 4 The derivative of a vector function
stich3 [128]

Answer:

r'(t)=(sin(6t)+6tcos(6t),2t,cos(7t)-7tsin(7t))

Step-by-step explanation:

We need to find the derivative r'(t) of the vector function :

r(t)=(tsin(6t),t^{2},tcos(7t))

In order to find r'(t), we are going to differentiate each of its components ⇒

We can write the following ⇒

r(t)=(f(t),g(t),h(t))=(tsin(6t),t^{2},tcos(7t)) ⇒

f(t)=tsin(6t)\\g(t)=t^{2}\\h(t)=tcos(7t)

Let's differentiate each function to obtain r'(t) :

f(t)=tsin(6t) ⇒ f'(t)=1.sin(6t)+t.cos(6t).6=sin(6t)+6tcos(6t) ⇒

f'(t)=sin(6t)+6tcos(6t)

Now with g(t) :

g(t)=t^{2} ⇒

g'(t)=2t

With h(t) :

h(t)=tcos(7t) ⇒ h'(t)=1.cos(7t)+t[-sin(7t)].7 ⇒

h'(t)=cos(7t)-7tsin(7t)

Finally we need to complete r'(t)=(f'(t),g'(t),h'(t)) with its components :

r'(t)=(sin(6t)+6tcos(6t),2t,cos(7t)-7tsin(7t))

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