Jack Sparrow and his crew snuck up on their enemies by submerging an upturned wooden rowboat and breathing in an air pocket in the upside-down boat's cavity.  What stupidly large force would be needed to hold such a boat underwater?  The total volume of the wood is 0.0686 m3 and the density of the boat is 380. kg/m3.  It will hold 5.28 m3 of air which has a density of 1.20 kg/m3.  The density of water is 1000. kg/m3.

A high-speed lifting mechanism supports an 881 kg object with a steel cable that is 22.0 m long and 4.00 cm^2 in cross-sectional area.  Young's modulus for steel is 20.0 ⋅10^10 Pa.  The elongation of the cable is 2.377x10^-3 m. By what  amount does the cable increase in length if the object is accelerated upwards at a rate of 3.11 m/s2?

Let us assume you are lifting out a 179 lb sheep. The density of the air around the balloon is 1.23 kg/m3 and the density of the air inside the balloon is 0.946 kg/m3.  If the sheep accelerates upwards at 4.84 m/s2, what is the volume of the balloon?  1 kg = 2.20 lbs

Air streams past a small airplane's wings such that speed is 50 m/s over the top surface and 30m/s past the bottom. If the plane has a wing of 9m^2. Ignoring the small height difference find 1.The pressure difference between the top and bottom of the plane's wings. 2. What would be the gravitational pull on the plane assuming the plane is moving horizontally. .

Draw a right-handed 3D Cartesian coordinate system (= x, y and z axes). Show a vector A with tail in the origin and sticking out in the positive x, y and z directions. Show the angles between A and the positive x, y and z axes, and call these angles α₁, α₂ and α3 Prove that Ax Acos α₁ Ay = Acos α₂ A₂- Acos α3

solve for Vo

Draw a third quadrant vector C. (remember that boldface characters represent vector quantities). Show the standard angle 0 for this vector (= angle that C makes with the positive x- axis). Also show the angle that C makes with the negative y-axis: call the latter angle 8. Finally, show the smallest angles that C makes with the positive x-axis and the positive y-axis: call these angles p1 and p2, repectively. a) Prove the following formulas for the components of C involving the standard angle (hint: start with the formulas for the components based on the angle & and then use (look up if necessary) co-function identities linking cosine and sine of 8 to sine and cosine of 0 since 8 = 3π/2-8 (this will switch cosine and sine around and eliminate - signs as well)) - C=Ccose C₁=Csine b) Prove the following formulas for the components of C: C=Ccosp1 C=Ccosp2

Notation matters when working with vectors! In particular, it is important to distinguish between the vector itself (A) and its magnitude (A). Illustrate in four separate sketches that each of the following statements is possible: a) both R = A + B and R=A+B are correct b) R = A + B is correct, but R=A+B is incorrect c) R = A + B is incorrect, but R=A+B is correct d) both R = A + B and R=A+B are incorrect

You know from your math courses that an infinitesimal segment of a circular arc can be considered as a straight line segment. Imagine that you cover a full circle in, say, the clockwise direction, with infinitesimal displacement vectors dr. Then evaluate fdr and fdr (the circle symbol on the integral just reminds us that we have to go around the full circle).