This problem is an example of critically damped harmonic motion. A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 5 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. Take as the gravitational acceleration 32 feet per second per second. (Note that the positive y direction is down in this problem.) y = le

Question 17 In casting metal parts, molten metal flows through a “gate" into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminum pistons examined 12 types formed from the same alloy. Say that we are interested in how the piston wall thickness (measured in inches) influences the gate velocity (measured in feet per second) chosen by the skilled workers who do the casting. The data is provided below. Thickness Velocity TII Velocity Thickness 0.248 123.8 0.628 326.2 0.359 223.9 0.697 302.4 0.366 180.9 0.697 145.2 0.400 104.8 0.752 263.1 0.524 228,6 0.806 302.4 0.552 223.8 0.821 302.4 Considering the coefficient of determination and regression equation and the scatterplot that this data would generate, what can we say about the linear relationship that the regression line provides? O The regression equation is 70.44 + 274.78x and the linear relationship explains about…

3.19 A cameraman is filming a marathon. He wants to keep his camera pointed at the lead runner, but since he is not allowed to leave his current location he must rotate the camera to keep the runner in frame. At the instant shown in Figure 3.23, 0 = 50°, the runner has a speed of 6.00 m/s and an acceleration of 0.10 m/s² to the left. What are the values of and Ö at this instant? camera 0,0 Vrunner 20m