Limits word problems (tow-rope release; helicopter jump)

[wind]

1. A ski boat travels in a parabolic curve. Let the vertex of the parabola be the origin and let the parabola open upward. the boat is currently at a point 100m west the 100m north of the origin, travelling toward the origin. The dack is situated 100m east and 50m north of the origin. At what point should the skier release the tow rope to heat straight for the dock?

I don't understand this question, I have a picture but i don't know how to solve this, can't the skier relese the roap at 50m west and 100m north of the origin and be headed straight for the dock...? But thats not the right answer so, can some onne please expalain this?

2. At a publicity event, Ayida, a stuntperson, will jump out of a helicopter with a jetpack on her back. The jetpack allows her to achieve a net upward acceleration of 4.4m/s^2 for a single interval of maximun lenght 10s. Ayida wants to time the use of the jetpack so that she lands with a zero velocity.
a) If the helicpter is 100m hight, when should Ayida turn on her jetpack? When will she land?
b) If the helicopter is 200m hight, when should Ayadia turn on her jetpack? when will she land?
c) What is the maximum height from wich Ayida can jump to land with zero velocity?

Again, I don't understand this question, v= change in displacement/ change in time
sooo...

v=0
t1= ?
t2= ?
d1= 100m
d2= 0m

but then there is also a jet pack....this question is confusing.

can someone please help me with these questions? Thanks

 

[galactus]

Re: Limits word problems

1. A ski boat travels in a parabolic curve. Let the vertex of the parabola be the origin and let the parabola open upward. the boat is currently at a point 100m west the 100m north of the origin, travelling toward the origin. The dack is situated 100m east and 50m north of the origin. At what point should the skier release the tow rope to heat straight for the dock?

I don't understand this question, I have a picture but i don't know how to solve this, can't the skier relese the roap at 50m west and 100m north of the origin and be headed straight for the dock...? But thats not the right answer so, can some onne please expalain this?

Well wind, start by finding the equation of your parabola.

You have a point on the parabola and the vertex. That's enough.

\(\displaystyle \L\\y=\frac{x^{2}}{100}\)......(verify)

In order for the skier to let go of the rope and head straight for the dock, he/she is going to have to be on a tangent to the parabola that passes through the dock at coordinates (100,50).

Find the derivative of the parabola: \(\displaystyle \L\\y'=\frac{x}{50}\).....(verify).

The thing is, we don't know where the tangent line meets the parabola that passes through the dock point(100,50)

Use the line formula: \(\displaystyle \L\\y-y_{1}=m(x-x_{1})\)

You have all the necessary data to solve for the x-coordinate where the tangent line meets the parabola.

\(\displaystyle \L\\\frac{x^{2}}{100}-50=(\frac{x}{50})(x-100)\)

Find x and y will follow.

 

[wind]

Thanks galactus.

Does anyone know about the 2nd one?