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ale4655 [162]
3 years ago
6

An object of mass 600 kg is released from rest 1000 m above the ground and allowed to fall under the influence of gravity. Assum

ing the force due to air resistance is proportional to the velocity of the object with proportionality constant bequals50 ​N-sec/m, determine the equation of motion of the object. When will the object strike the​ ground? [Hint: Here the exponential term is too large to ignore. Use​ Newton's method to approximate the time t when the object strikes the​ ground.] Assume that the acceleration due to gravity is 9.81 m divided by sec squared.
Mathematics
1 answer:
Deffense [45]3 years ago
5 0

Answer:

15 sec

Step-by-step explanation:

Data:

let m = 600 kg

    b  = 50

the differential equation will be:

m\frac{dv}{dt} = mg - bv(t)

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Let's call a child's ticket c and an adult's ticket a. From this, we can say:

c + a = 116,

since 116 tickets are sold in total.


Now, we are going to need to find another equation (the problem asks us to solve a systems of equations). This time, we are not going to base the equation on ticket quantity, but rather ticket price. We know that an adult's ticket is $17,000, and a child's ticket is thus

\$17000 \cdot (1 - \dfrac{1}{4}) = \$12750.


Given these values, we can say:

17000a + 12750c = 1653250,

since each adult ticket a costs 17,000 and each child's ticket c costs 12,750, and these costs sum to 1,653,250.


Now, we have two equations:

17000a + 12750c = 1653250

c + a = 116


Let's solve:

17000a + 12750c = 1653250

a = 116 - c

  • Find a on its own, which will allow us to substitute it into the first equation

17000(116 - c) + 12750a = 1653250

  • Substitute in 116 - c for a

1972000 - 17000c + 12750c = 1653250

  • Apply the Distributive Property

1972000 - 4250c = 1653250

  • Combine like terms

4250c = 318750

  • Subtract 1972000 from both sides of the equation and multiply both sides by -1

c = 75


We have now found that 75 child's tickets were sold. Thus,

75 + a = 116 \Rightarrow a = 116 - 75 = 41,

41 adult tickets were sold as well.


In sum, 41 adult tickets were sold along with 75 child tickets.

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