Encuentre el trabajo realizado cuando una particula se mueve en el campo de fuerzas \( F=3 x^{2} i+(2 x z-y) j+z k \) a lo bigo \( C \) de la curva en el espacio \( x=2 t^{2} \quad y=t \quad z=4 t^{2} \), cuando \( +E[0,1] \)

Water flows through a tube of diameter 2 cm at an average speed of \( 3 \mathrm{~m} / \mathrm{s} \). The end of the tube is closed with a plug with ten holes, each with a radius of 1 mm , calculate the speed of the water flowing from each hole

Free fall questions A ball is thrown directly downward, with an initial speed of \( 8.00 \mathrm{~m} / \mathrm{s} \), from a height of 30.0 m . After what time interval does the ball strike the ground? At \( t=0 \), a stone is dropped from the top of a cliff above a lake. Another stone is thrown downwar 1.6 s later from the same point with an initial speed of \( 32 \mathrm{~m} / \mathrm{s} \). Both stones hit the water at th same instant. Find the height of the cliff. A hoodlum throws a stone vertically downward with an initial speed of \( 12.0 \mathrm{~m} / \mathrm{s} \) from the roof of a building, 30.0 m above the ground. How long does it take the stone to reach the ground and What is the speed of the stone at impact respectively. An object is dropped from rest at a height of 120 m . Find the distance it falls during its final second in the air. A freely falling object requires 1.50 s to travel the last 30.0 m before it hits the ground. From what height above the ground did it fall? A ball is thrown directly downward, with an initial speed of \( 8.00 \mathrm{~m} / \mathrm{s} \), from a height of 30.0 m . Afte what time interval does the ball strike the ground? A stone is dropped into a river from a bridge 43.9 m above the water. Another stone is thrown vertically down 1.00 s after the first is dropped. The stones strike the water at the same time. What is the initial speed of the second stone? A bolt is dropped from a bridge under construction, falling 90 m to the valley below the bridge. (a) In how much time does it pass through the last \( 20 \% \) of its fall? What is its speed (b) when it begins tho last \( 20 \% \) of its fall and (c) when it reaches the valley beneath the bridge?

6) Oil flows through a tube at a rate of \( 6 \mathrm{Liter} / \mathrm{min} \), another tube is connected to it and the oil comes out of its nozzle at a speed of \( 4 \mathrm{~m} / \mathrm{s} \), calculate the cross-sectional area of the second tube 7) Water flows through a tube of diameter 2 cm at an average speed of \( 3 \mathrm{~m} / \mathrm{s} \). The end of

\( \begin{array}{ll}3.33 \text { • Uma canoa tem velocidade de } 0,40 \mathrm{~m} / \mathrm{s} \text { a sudeste em } & \text { Pa } \\ \text { relação à Terra. A canoa se desloca em um rio que escoa a } \\ 0,50 \mathrm{~m} / \mathrm{s} \text { para leste em relação à Terra. Determine o módulo, } \\ \text { a direcão e o sentido da velocidade da canoa em relacão ao rio. }\end{array} \)

Gasoline flows in a tube with a diameter of 2 cm at a speed of \( 5 \mathrm{~m} / \mathrm{s} \). Calculate: (a) The amount of gasoline flowing per minute. (b) The time required for a tank with a capacity of \( 20 \mathrm{~m}^{3} \) to be filled with gasoli (knowing that \( \pi=3.14 \) )