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- I. If s’(t) = v(t), and s’’(t) = a(t), use the fact that integration reverses differentiation (+C) and the given information about s(t) to find the particular solution to the following problem. If a model rocket’s velocity is given by a(t)= -32 m/s2 and v(0)= 10 and position at 1 second is 1,000 m, find s(t). Hint: Integrate a(t) to find v(t), then integratev(t) to find s(t), finding each C using the given info.A dolphin in an aquatic show jumps straight up out of the water at a velocity of 13.0 m/s. (a) List the knowns in this problem. (b) How high does his body rise above the water? To solve this part, first note that the final velocity is now a known and identify its value. Then identify the unknown, and discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking units, and discuss whether the answer is reasonable.Find the following for path C (a) the totaldistance traveled and (b) the magnitude and direction of thedisplacement from start to finish. In this part of the problem,explicitly show how you follow the steps of the analyticalmethod of vector addition
- If curve C at right is a graph of y velocity (in m/s) versus time, identify:a. Is acceleration ay positive, negative, or zero?b. Find the value of initial velocity vyoc. At what time does the body come to rest, for a moment?A person sitting in an enclosed train car, moving at constantvelocity, throws a ball straight up into the air in her referenceframe. (a) Where does the ball land? What is your answerif the car (b) accelerates, (c) decelerates, (d) rounds a curve,(e) moves with constant velocity but is open to the air?You drive a car 680 ft to the east, then 340 ft to the north. (a) Whatis the magnitude of your displacement? (b) Using a sketch, estimate the direction of your displacement. (c) Verify your estimatein part (b) with a numerical calculation of the direction.
- A person standing on the roof of a building 12 m high throws a ball upward with a velocity, Vₒᵧ = 22 m/s. Calculate (a) How high does the ball go with respect to the ground? and (b) What is the ball's velocity, V_fy, at impact?In adding Vectors in general, we follow the rule of a. Sin and Cos b. Paralellogram c. Pythagorean d. ComponentsDylan has an initial velocity of his slow walk at 5 ft/min^2, and he accelerated to running at 5 fraction numerator f t over denominator m i n squared end fraction for 4 seconds. How much distance did Dylan cover?
- A dolphin in an aquatic show jumps straight up out of thewater at a velocity of 13.0 m/s. (a) List the knowns in thisproblem. (b) How high does his body rise above the water?To solve this part, first note that the final velocity is now aknown and identify its value. Then identify the unknown, anddiscuss how you chose the appropriate equation to solve forit. After choosing the equation, show your steps in solving forthe unknown, checking units, and discuss whether the answeris reasonable. (c) How long is the dolphin in the air? Neglectany effects due to his size or orientationUnreasonable results A dolphin in an aquatic show jumps straight up out of the water at a velocity of 15.0 m/s. (a) List the knowns in this problem. (b) How high does his body rise above the water? To solve this part, first note that the final velocity is now a known, and identify its value. Then, identify the unknown and discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking units, and discuss whether the answer is reasonable. (c) How long a time is the dolphin in the air? Neglect any effects resulting from his size or orientation.A trapper walks a 5.0-km straigt4ine distance from his cabin to the lake, as shown in the following figure. Use a graphical method (the parallelogram rule) to determine the trapper’s displacement directly to the east and displacement directly to the north that sum up to his resultant displacement vector. If the trapper walked only in directions east and north, zigzagging his way to the lake, how many kilometers would he have to walk to get to the lake?