1. A model for the position x (t) of an Olympic jump skier says that the acceleration a(t) = x" is proportional to the square of the velocity v(t) = x'(t). Note this model comes from taking into account the friction of air against the skier, and we are greatly simplifying the problem by not taking into account gravity. In this problem, units of distance are in meters and units of time are in seconds. (a) Give an ODE in terms of v(t) only (meaning: no x or a) that corresponds to this model, and find its general solution v. (b) Recalling that our model comes from taking friction into account, which will slow down the skier, say whether you expect your proportionality constant from la to be positive or negative. (c) Use your solution v(t) from la to find x(t). (d) Use the initial conditions x(0) position of the skier. = 0 and v(0) = 100 to find the unique solution for x(t), the

You throw a ball of mass 1 kilogram upward from a height of 0 meters with a velocity of a = 23 m/s on Mars, where the acceleration due to gravity is g = 3.711 m/s. (a) Use your calculator to approximate how much longer (in seconds) the ball is in the air on Mars compared to on Earth where g = 9.80 m/s-. (Round your answer to three decimal places.) X S (b) Use your calculator to approximate how much higher (in meters) the ball went on Mars compared to on Earth. (Round your answer to one decimal place.) X m

Can I get an easy explanation

4 The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s=, where t is measured in seconds. Find the velocity (in m/s) of the particle at times t = a, t = 1, 2¹ t=2, and t = 3. t = a t = 1 t = 2 t = 3 y = V = V = V = m/s m/s m/s m/s

#17

In the previous Problem Set question, we started looking at the position functions (t), the position of an object at time t. Two important physics concepts are the velocity and the acceleration. If the current position of the object at time is as (t), then the position at time h later is a (t+h). The average velocity (speed) during that additional time his (s(t+h)-s(t)) If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h→0. i.e. the derivative a' (t). Use this function in the model below for the velocity function (). h The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a(t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t) = ✔ (t) =" (t). Problem set question: A particle moves according to the position functions (t) = etsin (2). Enclose arguments of functions in parentheses. For example, sin…

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