gradient

The following consecutive readings (in m) were taken with a dumpy level and a levelling staff at a common interval of 20 m: 0.385; 1.030; 1.925; 2.825; 3.730; 4.850; 1.045; 2.005;...

A car is travelling at a speed of 60 km/hr on a section of a National Highway having a downward gradient of 2%. The driver of the car suddenly observes a stopped vehicle on the car...

The longitudinal sections of a runway have gradients as shown in the table. End to end for sections of runway (m) 0 to 200 200 to 600 600 to 1200 1200 to 1600 1600 to 2000 Gradient...

A vector field $\vec{p}$ and a scalar field $r$ are given by $\vec{p} = (2x^2 – 3xy + z^2 ) \hat{i} + ( 2y^2 – 3yz + x^2 ) \hat{j} + (2z^2 – 3xz + x^2 ) \hat{k}$ $r = 6x^2 + 4y^2 –...

A bird is resting on a point P at a height of 8 m above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point Q whi...

A car is travelling at a speed of 60 km/hr on a section of a National Highway having a downward gradient of 2%. The driver of the car suddenly observes a stopped vehicle on the car...

A vector field $\vec{p}$ and a scalar field $r$ are given by: $\vec{p} = (2x^2 - 3xy + z^2) \hat{i} + (2y^2 - 3yz + x^2) \hat{j} + (2z^2 - 3xz + x^2) \hat{k}$ $r = 6x^2 + 4y^2 - z^...

A bird is resting on a point P at a height of 8 m above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point Q whi...

Let $\phi$ be a scalar field, and $\mathbf{u}$ be a vector field. Which of the following identities is true for $\text{div}(\phi\mathbf{u})$?

The longitudinal section of a runway provides the following data: End-to-end runway (m) | Gradient (%) ---|--- 0 to 300 | + 1.2 300 to 600 | - 0.7 600 to 1100 | + 0.6 1100 to 1400...

The directional derivative of the field $$u(x, y, z)=$$ $${x^2} - 3yz$$ in the direction of the vector $$\left( {\widehat i + \widehat j - 2\widehat k} \right)\,\,$$ at point $$(2,...

A straight 100 m long raw water gravity main is to carry water from an intake structure to the jack well of a water treatment plant. The required flow through this water main is 0....

For a scalar function $$f(x,y,z)=$$ $${x^2} + 3{y^2} + 2{z^2},\,\,$$ the gradient at the point $$P(1,2,-1)$$ is

For a scalar function $$\,f\left( {x,y,z} \right) = {x^2} + 3{y^2} + 2{z^2},\,\,$$ the directional derivative at the point $$P(1,2,-1)$$ in the direction of a vector $$\widehat i -...

The directional derivative of $$\,\,f\left( {x,y,z} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at the point $$P(2,1,3)$$ in the direction of the vector $${\mkern 1mu} \vec a = \wideha...

The directional derivative of the following function at $$(1, 2)$$ in the direction of $$(4i+3j)$$ is : $$f\left( {x,y} \right) = {x^2} + {y^2}$$

The directional derivative of the function $$f(x, y, z) = x + y$$ at the point $$P(1,1,0)$$ along the direction $$\overrightarrow i + \overrightarrow j $$ is

The derivative of $$f(x, y)$$ at point $$(1, 2)$$ in the direction of vector $$\overrightarrow i + \overrightarrow j $$ is $$2\sqrt 2 $$ and in the direction of the vector $$ - 2\o...

The required slope correction for a length of 60m, along a gradient of 1 in 20 is