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Q6. Find the gradient of the following functions
f(x, y, z) = x2y3z4.
f(x, y, z) = exsin(y) ln(z).
Q7. The height of certain hill (in feet) is given by h(x,y)=10(2xy−3x2 −4y2 −18x+28y+12)
Where y is the distance in north, x is the distance in east.
a. Where is the top of the hill located?
b. How high is the hill?
c. How steep is the slope (in feet per mile) at a point 1-mile north and 1- mile east, in what
direction is the slope steepest?
Q8. Calculate the divergence and Curl, of the following functions
a. V= x2 i+3xy^2 j -2xyz k
b. V=xyi+2yz j+3zx k
c. V= y2i +(2xy+z2)j+ 2yz k , where i , j , k are unit vectors along x, y and z axis
Let A= (3.0 m, 200 south of east), B = (2.0 m, north), and C= (5.0 m, 700 south of west).
a. Draw and label A , B, and C with their tails at the origin. Use a coordinate system with the x-axis to the east.
b. b. Write A, B, and C in component form, using unit vectors.
c. c. Find the magnitude and the direction of D = A + B+ C.
two wires A and B of the same material and equal lengths but of radii r and soldered coaxially the free end of B is twisted by an angle the ratio of the twist at the junction and angle phi is
An airplane takes off and flies 225 km on a course of 25.0° north of west and then changes direction and flies 135 km due north where it lands. Find the displacement from its starting point to its landing point
A boy travels 10m due north and then 10m due east. What is the displacement of body?
The velocity v of a wave in a stretched string depends on tension T, in the string and the mass per unit length U of the string.Obtain an expression for V in terms of T and U, using the method of dimensions
An object is shot from the ground into the air. Right at a speed of 50 m/s and an angle of 60 degrees above the horizontal it explodes. One fragment leaves the object to the left at a speed of 75 m/s and an angle of 45 degrees below the horizontal. What is the velocity of the fragment with respect to the ground?
1.5 kg and m2 -
3.0 kg are connected by a
thin string running over a massless pulley. One of the masses
hangs from the string; the other mass slides on a 35 ramp
with a coefficient of kinetic friction -
k -
0.40 (Fig. 6.33).
What is the acceleration of the masses?
A 9.00-kg hanging object is connected by a light,inextensible cord over a light ,frictionless pulley to a 5.00-kg block that is sliding on a flat table. Taking the coefficient of kinetic friction as -.200, find the tension in the string
