An object is dropped from a tower, 1936 ft above the ground. The object's height above the ground t seconds after it is dropped is s(t) = 1936-16t". Determine the velocity and acceleration of the object the moment it reaches the ground. The velocity of the object the moment it reaches the ground is | f/s. (Simplify your answer.) The acceleration of the object the moment it reaches the ground is fu/s2. (Simplify your answer.)350t - 501- A small probe is launched vertically from the ground. After it reaches its high point, a parachute deploys and the probe descends to Earth. The height of the probe above ground is s(1) = -, for 0 sts7. 1 + 1 a. Graph the height function and describe the motion of the probe. b. Find the velocity of the probe. c. Graph the velocity function and determine the approximate time at which the velocity is a maximum. a. Choose the correct graph of the height function below. O A. O B. O C. OD. Q [0,7,1] by [0, 180,5] [0,7,1] by [0,360, 10] [0,7,1] by [0, 180,5] [0,7,1] by [0,180,5] Describe the motion of the probe. Choose the correct answer below. O A. The probe launches upward at a decreasing rate over the first half of its trip. Then it reaches a peak and falls at a decreasing rate until it reaches the ground at 7 seconds. O B. The probe launches upward moving fastest at the beginning and slows over the first second. It peaks and begins to fall downward slowing as it gets closer to the ground until reaching the ground at 7 seconds. O C. The probe launches at a fast speed and slows at a decreasing rate over the first half of its trip. It begins to fall at an increasing rate until it reaches that ground at 7 seconds O D. The probe speeds up quickly over the first second, then begins to slow down over the first half of its trip. Then, the probe begins to fall at an increasing rate until the last second where it begins to slow down until it reaches the ground at 7 seconds. b. v(t) = c. Choose the correct graph of the velocity function below. O A. O B. O C. OD. Q [0,7,1] by [ - 180, 180, 10] [0,7,1] by [ - 180,370, 10] [0,7,1] by [ - 50,50,5] 10,7,1] by [ - 370, 180,10] The velocity is at a maximum at approximately t= ]- (Type a whole number.)The accompanying graph shows the position of a bicyclist after t hours. Assume s is positive when the bicyclist is east of his starting point. a. Determine the average velocity of the bicyclist over the first hour of the trip. Q O A. - 60 mph O B. 60 mph O C. 10 mph O D. - 10 mph Position (miles after t hours) b. Find the average velocity of the bicyclist over the time interval [1,2.5] O A. - 32 mph O B. -6.7 mph Time (hours) O C. 6.7 mph Using the graph, answer parts a through d. O D. 32 mph Is the average velocity a good estimate of the instantaneous velocity at t = 2 hrs? O No Yes c. Find the average velocity of the bicyclist over the time interval [2,3.5]. O A. - 12 mph O B. 12 mph O C. -4 mph O D. 4 mph Estimate the velocity of the bicyclist at t= 0.5 hours and determine the direction in which the bicyclist is moving. O A. 10 mph to the east O B. 2 mph to the west O C. 60 mph to the east O D. 10 mph to the west d. Describe the movement of the bicyclist during the 4 hour trip. O A. The bicyclist rides up a hill the entire time. O B. The bicyclist rides to the east, takes a break after two hours, and then rides to the west. O C. The bicyclist takes a curvy path, riding both to the east and to the west O D. The bicyclist rides to the east, takes a break after two hours, and then rides to the east again.Jean and Juan run a one-lap race on a circular track. Their angular positions on the track during the race are given by the functions ((1) and ((1), respectively, where Osts 12 min (see accompanying figure). These angles are measured in radians, where 0= = 0 represent the starting position and 0 = = 2x represent the finish position. The angular velocities of the runners are 0'(1) and '(t). Complete parts (a) through (e) below. Click the icon to view the figures of the angular positions of Jean and Juan. a. Compare in words the angular velocity of the two runners and the progress of the race. Choose the correct answer below. O A. Juan starts out faster, and then slows down. Jean starts out slower, and then speeds up. O B. Jean is always faster. O C. Jean starts out faster, and then slows down. Juan starts out slower, and then speeds up. O D. Juan is always faster. b. Which runner has the greater average angular velocity? O A. Both runners have the same average angular velocity. O B. Juan O C. Jean c. Who wins the race? A. Juan wins the race. O B. Jean wins the race. O C. The race ends in a tie. d. Jean's position is given by 0(t) = - 72 What is her angular velocity at t= 6 and at what time is her angular velocity the greatest? Her angular velocity at t = 6 is | min rad (Type an exact answer in terms of x.) Her angular velocity is the greatest at t= |] min. e. Juan's position is given by (t) = att(24 -1) 72 -. What is his angular velocity at t = 6 and at what time is his angular velocity the greatest? His angular velocity at t= 6 is | min rad (Type an exact answer in terms of A.) His angular velocity is the greatest at t = ] min.The graph of s = f(1) represents the position of an object moving along a line at time t 2 0. a. Assume the velocity of the object is 0 when t= 0. For what other values of t is the velocity of the object zero? b. When is the object moving in the positive direction and when is it moving in the negative direction? c. Sketch a graph of the velocity function d. On what intervals is the speed increasing? Q a. The velocity of the object is zero att = ]. (Use a comma to separate answers as needed.) b. When is the object moving in the positive direction? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The object is moving in the positive direction on the interval(s). Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a comma to separate answers as needed. Use integers or decimals for any numbers in the expression.) B. The object is never moving in the positive direction. When is the object moving in the negative direction? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The object is moving in the negative direction on the interval(s). (Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a comma to separate answers as needed. Use integers or decimals for any numbers in the expression.) O B. The object is never moving in the negative direction. c. Sketch a graph of the velocity function. Choose the correct graph below. O A. OB O C. O D. Q Q Q Q d. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The speed of the object is increasing on the interval(s). Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a comma to separate answers as needed. Use integers or decimals for any numbers in the expression. Use ascending order.) O B. The speed of the object never increases