a) A 4 kg cannonball is shot into the air with an initial upward velocity of +100 m/s. Assume the ball experiencesair resistance proportional to its velocity, given by a drag coefficient of b = 0.5 kg/s. At what time does it strike theground? ie, find x(t) = height of the ball at time t, and solve x(t) = 0. You may need a graphing calculator todetermine the intersection point.b) Draw a slope field for the equation ==dzy, within (at least) the range -2 ≤ x ≤2, -2 ≤ y ≤2

Answered: Image /qna-images/answer/24a53fc3-5709-4b66-8987-1f0844b56b77.jpg

Answered: a) A 4 kg cannonball is shot into the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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suppose the height of the golf ball t seconds after jt is hit is given by h(t)=-16t^2+48t+64 use your calculator to answer the following A) when dies the ball reach maximum height B) when does the ball strike the ground C) sketch the graph of the velocity it the ball between t=0 and t=4
The position of a honeybee flying up and down a straight flowerbed is given by (the euqation ) where t is measured in seconds and s is measured in meters. Positive values of s indicate that the bee is to the right of the center of the flowerbed, while negative values of s indicate that it is to the left of the center. (a) Use the graph to guess the time(s) at which the velocity of the bee is 0, and then use calculus to confirm the answer (b) How fast and in what direction is the bee flying at t = 3.5 seconds? (c) Find the velocity of the bee at all times when its acceleration is zero.
A trough is 2 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = foot-pounds required to empty the trough by pumping the water over the top. Note: In this problem, use 62 pounds per cubic foot as the weight of water. x from x = 1 to x = 1. The trough is full of water. Find the amount of work in 2 ft 1ft y = x8 foot-pounds US V O CO %23
A ramp in a skateboard park is modelled by a curve with equation f(x) = 10.67 -1.67x+0.0417x² where x is the horizontal distance in metres and f(x) is the height above the ground in metres. a Find the maximum depth of the run. b Find the x-intercepts and explain what these values represent.
The equation of a curve is y=4x²+ 4lx+12-k, where kis a constant. In the case where k =1, find the equation of the tangent to the curve which is parallel to the x-axis.
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.
The total fresh vegetables consumed per person per year can be modeled by V(t) = 0.2(t- 2)² + 64.8 where V(t) is the total fresh vegetables consumed per person in pounds per year t years since 2013. Find when the minimum intake of fresh vegetables per person occurred? {final answer will be just number only}
The respiration rate R (in litres/min) of a boy can be modelled by the equation R = 6-3 cost, where t is the time (in minutes) at which the respiration rate is measured. (i) Explain why this model suggests that the respiration rate, R (in litres/min) of the boy is 3
solve

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