Exercise 0.1.1 The trough shown in the image below is constructed by fastening together three slabs of wood of dimensions 10 ft by 1 ft, and then attaching the construction to a wooden wall at each end. The angle 0 was originally 30°, but because of poor construction the sides are collapsing. The trough is full of water. At what rate (in ft° /sec) is the water spilling out over the top of the trough if the sides have each fallen to an angle of 45°, and are collapsing at the rate of 1° per second? 10

4. The boat is travelling at 18 knots on a heading of 234°. The current is 8 knots, flowing from a bearing of 125°. Determine the resultant velocity of the boat. You can use a trigonometry method or rectangular components method, but the final answer needs to be written in the same form as the original question.

Now measure and record the period for small angle motion with a stopwatch (there is no angle too small, so long as you can see it move). Measure the period in the following way: Move the mass away from equilibrium. Start a stopwatch and simultaneously release the mass. Stop the stopwatch after it swings 5 times back and forth. Record this value. Now acquire 5 more periods this way (each with five swings) so that you have six measures of the period of the same pendulum. Q2: What is the period of the pendulum written as mean +/- error while using a 95% confidence interval? Measurement #1: 3.17 Seconds (Period - T=0.634) Measurement #2: 2.95 Seconds (Period - T=0.590) Measurement #3: 3.25 Seconds (Period - T=0.650) Measurement #4: 3.16 Seconds (Period - T=0.632) Measurement #5: 3.17 Seconds (Period - T=0.634) Measurement #6: 3.22 Seconds (Period - T=0.644) Mean = 3.784/6=0.630 I do not understand how to produce the error +/- while using the 95% confidence interval. Could you please help…

A cylindrical bucket will hold 247 in°of water. It is $0.01/per in to create the bottom and side of the bucket and $0.02/per in? for the top. What radius and height would be the cheapest to make?