This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. If an arrow is shot upward on Mars with a speed of 55 m/s, its height in meters & seconds later is given by y = 55t - 1.86+2. Exercise (a) Find the average speed over the given time intervals. (i) [1, 2] [1, 1.5] (iii) [1, 1.1] (iv) [1, 1.01] [1, 1.001] Step 1 Recall that the average speed between times ti and to is calculated using "ave = Y(2) - y(t1) 2 - t1 We are given that y = 55t - 1.86t2. Evaluating at t = 1, we have y(1) = 55(1) - 1.86(1)2 = 53.14. Thus, the average speed between times 1 and 1 + h is as follows. Wave = Y(1 + h) - y(1) (1 + h) - 1 = 155(1 + h) - 1.86(1 + h)2] - 53.14 51.28h - 1.86 1.86 h2 = 51.28 51.28 - 1.86 $ 1.86 h, h =0 Step 2 To calculate the average speed for the time period [1, 2], we substitute h = 1 into Vave = 51.28 - 1.86h, and evaluate. Wave = 51.28 - 1.86(1) = 51.28 - 1.86 = 49.42 49.42 m/s (rounded to two decimal places) Similarly, for the time period [1, 1.5], we have Vave = 51.28 - 1.86(0.5) = 51.28 - 0.93 0.93 (do not round) = [50.35 50.35 m/s (rounded to two decimal places). Step 3 Using the same method, for the time period [1, 1.1], we have Wave = 51.28 - 1.86(0.1 8 .1 ) = 51.094 51.09 m/s (rounded to two decimal places). Step 4 Next, for the time period [1, 1.01], we have Vave = 51.28 - 1.86(0.01) = 51.2614 51.26 m/s (rounded to two decimal places). And finally, for the time period [1, 1.001], we have Wave = 51.28 - 1.86 0.001 001 = 51.27814 51.28 m/s (rounded to two decimal places). Exercise (b) Estimate the speed when t = 1. Step 1 To estimate the speed when & = 1, we need to estimate Vave = 51.28 - 1.86h when h approaches . This yields Vave = m/s