Derive differential equations. 1(1) m2
Q: the 8 ball into the top right corner pocket to win the game, but you want to make sure that you…
A: Solution: From the above-given data, Mass (m)=0.15 kg Time(∆t)=0.1 s Let us draw a figure to…
Q: 11) How fast is the balling moving when it reaches the bottom of the ramp? 4.2 kg sphere 12.2 m 350
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: A capacitor with an initial potential difference of 75 V is discharged through a resistor when a…
A: Given: In this question, The capacitor with an initial potential difference , Vo=75V is discharged…
Q: 4 i + V41 Suppose i -k and u = 2i + 5j. Compute the following: %3D %3D V41 lū| = %3D ... II
A: Given: v→=441i+541ju→=2i+5j
Q: 13
A: We are given a boat. We are also 2 forces acting and their directions also. We are given net force…
Q: Given P = 32 u, 90° N of E and R = 12 u, 45° N of E, find P - R in unit-vector form. Use the…
A: Given:P→ = 32 u, 90° North of EastR→ = 12 u, 45° North of East
Q: Given the function D= 3x²y - y³z², find the gradient VQ. b. a. 6xyî+ (3x² - 3y²z²)ĵ- 2y³zk…
A: Given, Φ = 3x2y - y3z2
Q: Let A=5i-6.5 and B=3.5i-7ĵ . If lies in the xy-plane, Cis perpendicular to À , and Č-B=15 , what is…
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Q: Four vectors: a´ = [1 2 3], b´ = [1 0 -1], c´ = [1 2 3 4], d´ = [2 1]. Compute each of the…
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Q: Determine the unit vector UA/O in the direction of ra/o. Answer: UA/O = (i i+ i j+ i k)
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Q: Let /be the line through the point with coordinates (0,1,0) in the direction of the vector 1 0 their…
A: Given, l be the line through the point with coordinates (0,1,0) in the direction of the vector…
Q: Suppose that you have two vectors (1,0,0, 1) (2,0,0, 2) at What is a"b,?
A: Given that aμ=(1,0,0,1) and bμ=(2,0,0,2) we have to find the value of aμbμ
Q: These are the component forms of vectors u and w: ū u = (1, 1) w = (2, 4) Subtract the vectors. ū -…
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Q: Problem 2 (Nodal Analysis): Find V. Express the result in polar form. j4 Q + Vx 2/0° A 5Ω -j3 2 (4)…
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Q: Assume = 36 and H = 4. Determine the x-component of H.
A: Given: The angle is alpha = 36 degree The magnitude of the vector H = 4 units
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- A.) i. Define the plane polar unit vectors ŕ and 0 and show that they are orthonormal. Determine dr dê and de de ii. Hence show that for the vector r(t) = r(t)ŕ dr · = rî +rðê, d²r and = - dt dt² († − rė²)ŕ + (2ŕė +rë)ê . iii. If a mass m moves in the plane along r(t) = a and (t) = 5t determine the shape of the motion and find its period. B) Show that the motion of an object under the universal gravitational force μη Fg is governed by the radial and angular equations of motion and μ = 0, 2r0+ rö = 0. Setting r(t) =R for some constant R, solve these equations of motion and determine the period of the motion. C) Consider the following non-linear differential equation *+5= x +4. Find the stationary solutions. Expand around each of the stationary so- lutions that you have found, in order to determine if they correspond to stable or unstable equilibria. D) Show that 1 5 E = 2 - 4x is a conserved quantity. Hence draw the phase-space diagram and de- termine for which values of E oscilations…97 PROBLEMS 2-45. Describe how to determine whe ther an equilibrium is stable or unstable when (dUdx),0. 2-46. Write the criteria for determining whether an equilibrium is stable or unstable when all derivatives up through order n, (d" U/ dx ") 0. 247. Consider a particle moving in the rCrionUse Stokes' theorem to evaluate SF. dr where F = z²î + y²ĵ + xk and C is the triangle with vertices (1, 0, 0), (0, 1, 0), and (0, 0, 1). The unit vector normal is upward. Z -3 2 2 X
- CLO 4 If the plane x+y+z-1=0 cuts the x-axis, y-axis, and z-axis at A, B, and C respectively. Find the perpendicular distance to the point P(2,6,9). В а. 9.24 b. 8.66 С. 9.81 d. None of the choices О е. 5.33 f. 5.67 N.Calculate the angle between the vectors A=(5;4) and B=(2;8)6. Given vectors Ã= 2â, + 4ây + 10â, and B = -5âp + âo – 3âz, find (a) Ã+ B at P(0, –2,5) , with o = 90° (b) ÷Ē (c) Ã× B (d) The angle between A and B at P (e) The scalar component of A along B at P
- The force P of magnitude 50 KN is acting at 215° from the x-axis. Find the components of P in u 157° from x, and v negative 69°from x. (Draw the Figure)3. Let a, b, n be integers, with n > 0. Prove that a = b (mod n) if and only if a² + b² = 2ab (mod n²).Question 4 Show that ǝ\rho (x, t) Ət + d√(x, t) dx = 0.