# Math Help - acceleration motion problem.

1. ## acceleration motion problem.

I got most of them this weekend. There's just a few I'm not sure about.

1. NASA launches a rocket at seconds. Its height, in meters above sea-level, as a function of time is given by .
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?

The rocket splashes down after ______ seconds.

How high above sea-level does the rocket get at its peak?

The rocket peaks at _______ meters above sea-level.

2.Solve the equation by factoring.
I know that one of the solutions is definitly -8. The other one I'm getting 5/4 but it says that's wrong.

3.Complete the equation of the circle centered at (-1,-1) with radius 6.
I'm getting 34=0 for this but I'm not to sure what the equation for a cirlce is.

4.A vendor sells ice cream from a cart on the boardwalk. He offers vanilla, chocolate, strawberry, blueberry, and pistachio ice cream, served on either a waffle, sugar, or plain cone. How many different single-scoop ice-cream cones can you buy from this vendor?
Do I use nPr or nCr for this one? And which number equals n and which one equals r.

5. The angle of elevation to the top of a building is found to be 13 degrees from the ground at a distance of 4500 feet from the base of the building. Find the height of the building.
I got 2 answers for this. 385205.8259 or 1038.90686

2.Solve the equation by factoring.
I know that one of the solutions is definitly -8. The other one I'm getting 5/4 but it says that's wrong.
$4x^2+37x+40=(x+8)(4x+5)$

x+8=0 -> x=-8
and
4x+5=0 -> x=-5/4

3. I figured out number 4 so I don't need help on that one.

1. NASA launches a rocket at seconds. Its height, in meters above sea-level, as a function of time is given by .
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?

The rocket splashes down after ______ seconds.

How high above sea-level does the rocket get at its peak?

The rocket peaks at _______ meters above sea-level.
Splashdown:
We are looking for a point in time where the rocket is at sea level. So we need:
$h(t) = -4.9t^2 + 67t + 241 = 0$

$t = \frac{-67 \pm \sqrt{67^2 - 4 \cdot (-4.9) \cdot 241}}{2 \cdot (-4.9)}$

I get that t = -2.95738 s or t = 16.6308 s. We may discard the negative time as unphysical.

Maximum height:
We are looking for a point in time where the vertical speed is zero (momentarily). So we set the first derivative of the height function to zero:
$h'(t) = -9.8t + 67 = 0$

$t = 6.83673 \, s$

This is WHEN the rocket reaches maximum height, so what is the maximum height?
$h(6.83673 \, s) = 470.031 \, m$

-Dan

5. I also figured out number 5

3.Complete the equation of the circle centered at (-1,-1) with radius 6.
I'm getting 34=0 for this but I'm not to sure what the equation for a cirlce is.
The general equation for a circle centered at (h, k) with radius r is:
$(x - h)^2 + (y - k)^2 = r^2$

$(x + 1)^2 + (y + 1)^2 = 36$

-Dan

7. Topsquark, It says that 6.83673seconds is wrong. The other part is right though.

8. Originally Posted by topsquark
The general equation for a circle centered at (h, k) with radius r is:
$(x - h)^2 + (y - k)^2 = r^2$

$(x + 1)^2 + (y + 1)^2 = 36$

-Dan
It has to equal 0. What would it be? 2x^2+4x-32 is what i get and it's wrong.

9. Originally Posted by topsquark
Splashdown:
We are looking for a point in time where the rocket is at sea level. So we need:
$h(t) = -4.9t^2 + 67t + 241 = 0$

$t = \frac{-67 \pm \sqrt{67^2 - 4 \cdot (-4.9) \cdot 241}}{2 \cdot (-4.9)}$

I get that t = -2.95738 s or t = 16.6308 s. We may discard the negative time as unphysical.

Maximum height:
We are looking for a point in time where the vertical speed is zero (momentarily). So we set the first derivative of the height function to zero:
$h'(t) = -9.8t + 67 = 0$

$t = 6.83673 \, s$

This is WHEN the rocket reaches maximum height, so what is the maximum height?
$h(6.83673 \, s) = 470.031 \, m$

-Dan