Problem 4. A scientist is testing the properties of a dense meteorite. The force of attraction F (in Newtons) between an object with mass m (in kilograms) and the meteorite when they are dmeters apart is defined by the formula belowm.F = f(m, d) = 1000-d2(a) Compute fa(80, 30) and interpret what it means in context of this situation. Round any numbers to three decimals(b) Construct a linear approximation L(m, d) for the force of attraction for a 50 kilogram object that is 40 meters away from the meteorite. Compute L(48, 41) and interpret what thismeans in context of the situation.

Here, F=f(m,d) represents force between an object with mass m and the meteorite when they are d…

Answered: Problem 4. A scientist is testing the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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
ll.2
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…
The amount of time it takes to drive somewhere is inversely proportional to the speed at which you drive. The time of a trip is 3 hours when you drive at 60 km/h. a) Determine the equation for the function t(v), which relating the time of the trip ("t", in hours) to the speed (v, in km/h). b) Find the time it would take to complete the above trip if you drove at 90 km/h. c) What speed should you drive at to complete the trip in 75 minutes? 2.

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