1. A fireworks shell is shot straight up with an initial velocity of 80 feet per second. Its height s after t seconds is given by the equation  s = 80t − 16t2.  If the shell is designed to explode when it reaches its maximum height, how long after being fired, and at what height, will the fireworks appear in the sky? time    ............  sec height   ..........   ft   2. A farmer wants to fence in three sides of a rectangular field shown below with 1,020 feet of fencing. The other side of the rectangle will be a river. If the enclosed area is to be maximum, find the dimensions of the field. smaller side ............    ft larger side..................  ft

Q: b) Find the temperature u(x,t) from the heat equation in a laterally insulated copper bar 80 cm long…

A: b) Given :-  The temperature ux,t from the heat equation in a laterally insulated copper bar 80 cm…

Q: 11. The position of a particle as it moves horizontally is described by the given equation S=sint…

A:

Q: From a lighthouse, ship A is at a distance of 6 √5 miles and on a bearing of 040° and ship B is at a…

A:

Q: Two particles have positions at time t seconds given by the equations s1 = t3 - t meters and s2 =…

A: V=d[S]/dt a=d[v]/dt

Q: If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool to…

A: From Newton’s Law of Cooling, we know that T(t) = Ts + Cekt Given C = 100, k = 0.1 Consider freshly…

Q: 2. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s , its height ( in meters)…

A:

Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s?, where k is a…

A:

Q: If a ball is given a push so that it has an initial velocity of 5 m/s down a certain inclined plane,…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10- 5t, where 0 <t <1.5 (in…

A:

Q: 2) The number of cells in a bacterial culture increases rapidly but then levels off. The amount is…

A: This question is about application of derivative.

Q: 12. The position of an object at time tis given by x = V3t – 4 ++4, where x is in feet and t is in…

A: (12) The position of an objects at time t is given by  xt=3t-4+1x+4, x is in feet and t is in…

Q: 2. A body moves along the straight path. If the given initial velocity is 2t2 – 4t + 5, what is the…

A: Given initial velocity is     vt = 2t2-4t+5As we know that velocity is rate of change of…

Q: ,2_2t A particle moves along a straight line with a velocity v(t) = t²e²¹ meters per second after t…

A:

Q: 2. A rock thrown upward has a height given by s(1) = 49t-9.81 where s is in meters and / is in…

A: Use derivative to solve

Q: 1. If a stone is thrown vertically upward frosthe surface of the moon with a velocity of 10 meters…

A: Follow the procedure given below.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 15 – 2t, where 0 ≤ t ≤ 3…

A: Here, the displacement is: S(t)=-t2+15t

Q: it is known from experiments that the height (in meter) of a certain plant after t months is given…

A: Given: ht=t-t; 0≤t≤1 for finding given values, first we draw graph of given function on given…

Q: 4. A certain particle is travelling in a straight line governed by the equation a = v5 m / s?. If…

A: we know the first equation of motionv=u+atv=1+2v95  m/s

Q: Using the method of undetermined coefficients, write the form of the assumed particular solution for…

A: Given: y"+2y'+y=x2e-x Auxiliary equation are,  m2+2m+1=0 (m+1)2=0 m=-1,-1

Q: A ball is thrown upward from a height of 6.5 m at an initial speed of 61 m/sec. Acceleration…

A: here we have .................initial height .................initial velocity ..............gravity

Q: 1. An arrow is shot vertically up into the air with an initial vertical velocity of 60 m/s, and its…

A: Given; Initial velocity=60m/s   h=-5t2+60t.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 5t, where 0 ≤ t ≤ 1.5…

A: The answer as follows:

Q: The position of a particle at any timet is given by S =-15t2+ 48t-10. What is the velocity after 10…

A: The given question is taken from the physics  in which we have to find the velocity of the particle…

Q: The equations for free fall at the surfaces of Mars and Jupiter (s in meters, t in seconds) are s =…

A: Consider the provided equation of free fall at the surfaces of Mars and Jupitar are shown below,

Q: A particle is moving along the x-axis so that at any time t > 0, its acceleration is given by the…

A: The acceleration of a particle is the rate of changing of velocity at time. When the velocity…

Q: The velocity of particle A, t seconds after its release is given by va(t) =2.Se0.5t meters per…

A: .

Q: If a rock is thrown vertically upward from the surface ofMars with velocity 15 m/ s  , its height…

A: Given that a rock is thrown vertically upward from surface of Mars with velocity 15 m/s. Its height…

Q: The number of cars produced when x dollars is spent on labor and y dollars is spent on capital…

A:

Q: If a cannonball is shot directly upward with a velocity of 144 ft per second, its height above the…

A: This question is about application of derivative

Q: solve the given initial value problem. Describe the behavior of the solution as t → ∞.…

A:

Q: An object is thrown upward at a speed of 70 feet per second by a machine from a height of 13 feet…

A:

Q: The equation of motion of a mass is given as: y = (0.51)e 0.-(0.01)e0.2, where y is the displacement…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: 1.) The height above the ground at which a ball is released at an initial height of 122.5m is given…

A:

Q: Consider the two tanks shown in figure.The tank A Contains 50 gallons of water in which 25 Ib of…

A: In the given question we have to find the equation at t time for tank A.

Q: If a rock is thrown vertically upward from the surface of Mars with velocity 15 m/s, its height…

A: Given:         h=15t-1.86t2    Height of rock h(t)=25m        15t-1.86t2=25   rewrite in the form of…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 14 - 6t, where 0 < t < 1.5…

A:

Q: Find the complementary function Yc, the particular solution Yp and the general solution of the…

A: Given that, y''+y'-6y=e-t+t

Q: Consider the two tanks shown in figure.The tank A Contains 50 gallons of water in which 25 Ib of…

A:

Q: The upper end of the ladder 5 m long leans against a vertical wall. Suppose the foot of the ladder…

A:

Q: If an object is projected upward from ground level with an initial velocity of 160ft per​ sec, then…

A: given  s(t)=−16t^2+160t

Q: A ball is thrown upward from a height of 4.6 m at an initial speed of 48 m/sec. Acceleration…

A:

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A: Given : pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of amole…

Q: 4- The motion of a particle is described by the equation x = a + bt where a =15cm and b 3cm. find…

A: 4.  Given equation of motion of particle:-                                                  x=a+bt2

Q: 21. If a stone is thrown vertically upward from the surface of the moon with a velocity of 10 m/s,…

A:

Q: 1. The position of the particle is given by the equation s = f(t), being s= t3 - 6t? + 9t, where t…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: The equation of motion of a mass is given as: y= (0.51)e 0.-(0.01)e.2. where y is the displacement…

A: The Newton-Raphson method uses the formula: tn+1=tn-f(tn)f'(tn) to perform the iterations and to…

Q: y = Ae* + Bre

A:

Q: A manufacturer can produce 4860 cell phones when I dollars is spent on labor and y dollars is spent…

A: Given ,

Q: If a cannonball is shot directly upward with a velocity of 304 ft per second. its height above the…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.