(3) Two vertical forces are applied as shown to boom AB which is supported by a ball-and-socket joint at A and cables BC and DE. The weight of the boom is negligible and cable DE is horizontal along the x-axis. Determine the tension forces T1 and T2 in the cables. Ans: T₁ 91.5 kN, T₂ = 53.3 kN 4 m 3 m 4 m T2. D T₁₂ H/2m 3 m 20 kN 30 kN

A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope. Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2 Express the forces in component form, in terms of θ and unknown magnitudes where appropriate. Write down the equilibrium condition for the basket and hence show that tan θ = 0.45. Determine the angle, in degrees, that the slope makes with the horizontal.

(6) A force of 200 N is applied perpendicular to the wrench at its tip as shown. Determine the equivalent force-couple system at center O of the wheel. Ans: F=68.4-187.9 N, Mo = 78.3 N'm CW 650 mm 125 mm 450 mm 20° 200 N

(4) A force F is applied through the bar on the slider at A as shown. If the t-component of the force is Ft = 90 N, determine the n-, x-, and y-components of the force F. Ans: Fn=-107.3 N, Fx = 131.6 N, Fy = -47.9 N F 20° n 30°

Suppose the elevation z above a point (x, y) in a horizontal xy- plane at sea level is z = 5cos (0.01(x? + y²)) meters. The positive x-axis points east, and the positive y-axis point north. A climber is at the point (6, 8, 2.70). If the climber uses a compass reading to walk southwest, will he ascend or descend? At what rate? Give your answer rounded to the nearest hundredth, and explain what the units are.

A skydiver weighing 120kg drops vertically from a jet flying at 4.000m. Assume the force due to air resistance to be proportional to the velocity of the skydiver, with the proportionality constant b1= 20 N⋅sec/m before the cute is opened, and b2= 100 N⋅sec/m after the chute is opened. If the skydiver opens the chute after 60 seconds of free fall, find:  a. The total amount of time elapsed between dropping out of the plane and landing.  b. The velocity of the skydiver at the instant of landing on the ground.

A 68 kg skydiver jumps out of an airplane. We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude cv² where c = 0.175 kg and v(t) is the velocity of the skydiver at time t (and upward is positive velocity). The gravitational constant is g = 9.8m/s². m a) Find a differential equation for the velocity v : dv dt b) Determine the terminal velocity in meters per second for free-fall (no parachute). terminal velocity= m/s Note: Answer should be negative for downward velocity.