1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ulleksa [173]
3 years ago
11

Explorers on a planet with a thin atmosphere want to measure the acceleration of gravity at its surface. So they use a spring gu

n to launch a ball bearing vertically upward from the surface with a launch velocity of 29 ms. If we denote by gs the acceleration of gravity in that planet, in ms2, then the ball bearing will move following the formula:
s(t) = 30(t) - [gs/2][t^2]

If the ball bearing reaches its maximum height 21 seconds after being launched, what is the value of gs?
Mathematics
1 answer:
Murljashka [212]3 years ago
5 0

Answer:

The value of g_s is g_s=\frac{30}{21} \:\frac{m}{s^2}.

Step-by-step explanation:

We know that the position function is given by

s(t)=30t-\frac{g_s}{2} t^2

Velocity is defined as the rate of change of position. Therefore,

v(t)=\frac{d}{dt}(s(t))

So, the velocity function is

v(t)=\frac{d}{dt}(s(t))\\\\v(t)=\frac{d}{dt}(30t-\frac{g_s}{2} t^2)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(30t\right)-\frac{d}{dt}\left(\frac{g_s}{2}t^2\right)\\\\v(t)=30-g_st

When a body reaches a vertical velocity of zero, this is the maximum height of the body and then gravity will take over and accelerate the object downward. Thus,

v(t)=30-g_st=0\\\\g_s=\frac{30}{t}

We know that the ball bearing reaches its maximum height 21 seconds after being launched (t = 21 s).

So, the value of g_s is g_s=\frac{30}{21} \:\frac{m}{s^2}.

You might be interested in
If a line has a slope of 4 and contains the point (-2, 5), what is its equation in point-slope form?
Sveta_85 [38]

Answer:

The equation of the line is y = 4x + 13

Step-by-step explanation:

In this question, we want to write the equation of the line using the point slope form.

Mathematically, the point slope form can be represented as;

(y-y1) = m(x - x1)

where x1 = -2 , y1 = 5 and m which is the slope is 4

Plugging these values into the equation, we have;

(y-5) = 4(x - (-2))

y-5 = 4(x + 2)

y -5 = 4x + 8

y = 4x + 8 + 5

y = 4x + 13

8 0
3 years ago
Use the law of Sines to find the missing angle of the triangle. <br> Find m
Whitepunk [10]
Ah...Trigonometry is fun!

The law of sines states:
\frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c}
The transitive property (switching the orders of the equations) applies here. Therfore, we can say that \frac{sinA}{a}=\frac{sinC}{c}

We then plug in our given values to find C

\frac{sin24}{77}=\frac{sinC}{162}
\frac{162*sin24}{77}=sinC
Solving, we get 0.8557316387. We're not done yet!

We are trying to find an angle measure, so we'll do the inverse of the ratio we used (sin).

arcsin0.8557316387 (arcsin is the same as inverse sin)
=58.8 (approximate)

So the measure of angle C is 58.8. You could check this by reinserting it into the equation \frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c}.

:)
6 0
3 years ago
Lead metal can be extracted from a mineral called galena, which contains 86.6% lead by mass. A particular ore contains 68.5% gal
r-ruslan [8.4K]

Answer:

ds hj bfsj gjhbyuabfdbsybfy

Step-by-step explanation:

sdbhabjbgfybsbfsad gfhysabfubdfr

6 0
3 years ago
-4x + 11y = 15<br> X = 2y <br><br> Solve using substitution <br><br> X = <br><br> Y=
Virty [35]
-4(2y)+11y=15, -8y+11y=3y=15: y=5

X=2(5)=10

To check your work -4(10)+11(5)=15
15=15
8 0
2 years ago
4. Small Town USA has a population of 3 x 102, Big Town has a population of 6 x 105,
zvonat [6]

Answer:

2.06

Step-by-step explanation:

3x102=306

6×105=630

630 ÷ 306 = 2.0588235294

round it to 2.06

4 0
2 years ago
Other questions:
  • A board game has a spinner divided into sections of equal size. Each section is labeled with a number between 1 and 5. Which num
    10·1 answer
  • The function h=−16t2+26t models the height h (in feet) of the dolphin after t seconds. after how many seconds is the dolphin at
    15·2 answers
  • 4 times as much as 3 is
    6·2 answers
  • Donner Summit, California, is a popular ski resort area. Over the past 60 years, the annual snowfall totals of Donner Summit hav
    11·2 answers
  • R = 20 : ((3/7) x 10)
    8·1 answer
  • Which statement is incorrect?
    12·1 answer
  • Please help with the math problem shown in the image
    13·2 answers
  • Joy uses 9.5 pints of blue paint and white paint to paint her bedroom walls. 3 5 of this amount is blue paint, and the rest is w
    10·1 answer
  • Derivative using direct definition of derivative 2-x/2+x
    10·1 answer
  • Solve for m:<br> (-11/6) + m = -2/9<br> M=
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!