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
DanielleElmas [232]
2 years ago
10

The force of gravity on Mars is different than on Earth. The function of the same situation on Mars would be represented by the

parabolic function shown below. On which planet would the ball go the highest? On which planet would the ball take the longest to return to the ground? Explain your reasoning.
Mathematics
1 answer:
sweet-ann [11.9K]2 years ago
3 0

Answer:

If thrown up with the same speed, the ball will go highest in Mars, and also it would take the ball longest to reach the maximum and as well to return to the ground.

Step-by-step explanation:

Keep in mind that the gravity on Mars; surface is less (about just 38%) of the acceleration of gravity on Earth's surface. Then when we use the kinematic formulas:

v=v_0+a\,*\,t\\y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2

the acceleration (which by the way is a negative number since acts opposite the initial velocity and displacement when we throw an object up on either planet.

Therefore, throwing the ball straight up makes the time for when the object stops going up and starts coming down (at the maximum height the object gets) the following:

v=v_0+a\,*\,t\\0=v_0-g\,*\,t\\t=\frac{v_0}{t}

When we use this to replace the 't" in the displacement formula, we et:

y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2\\y-y_0=v_0\,(\frac{v_0}{g} )-\frac{g}{2} \,(\frac{v_0}{g} )^2\\y-y_0=\frac{1}{2} \frac{v_0^2}{g}

This tells us that the smaller the value of "g", the highest the ball will go (g is in the denominator so a small value makes the quotient larger)

And we can also answer the question about time, since given the same initial velocity v_0 , the smaller the value of "g", the larger the value for the time to reach the maximum, and similarly to reach the ground when coming back down, since the acceleration is smaller (will take longer in Mars to cover the same distance)

You might be interested in
Please help!!!! No explanation needed <br> Help is appreciated
Elodia [21]

Answer:

A

-Brain Indigo

8 0
3 years ago
Write an equation and solve.
Reil [10]
My equation was (1230÷3) ×4 ×this is the multiplication sign

4 0
2 years ago
Please help and explain how to solve these! Thanks
spin [16.1K]
2. C
Slope = 40/8 = 5
Slope of graph c = 5/1 = 5

3. D
Slope = 9/3 = 3
Slope of graph d = 81/27 = 3
3 0
2 years ago
Read 2 more answers
Find the integral using substitution or a formula.
Nadusha1986 [10]
\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx

Derivative of the denominator:
\rm (x^2+2x+5)'=2x+2

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx

and then split the fraction,

\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx

Based on our previous test, we know that a simple substitution will work for the first integral: \rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx

So the first integral changes,

\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx

integrating to a log,

\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2

So we have this going on,

\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx

Bringing all that stuff together as a single square,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx

Making the substitution: \rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx

giving us,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du

simplying a lil bit,

\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du

and hopefully from this point you recognize your arctangent integral,

\rm ln|x^2+2x+5|+\frac52arctan(u)

undo your substitution as a final step,
and include a constant of integration,

\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c

Hope that helps!
Lemme know if any steps were too confusing.

8 0
3 years ago
Find the hcf of 24x3yz4,30x2y2z3 and 36 x3y2z3
dusya [7]

Answer:

8xyz

Step-by-step explanation:

multiply all numbers and alphabets

  1. 288xyz, 2.360xyz, 3.648xyz
  2. find HCF of numbers and after multiply by xyz
  3. 288={2×2×2×31}
  4. 360={2×2×2×3×3×5}
  5. 648={2×2×2×3×3×3×3}
  6. HCF={2×2×2}xyz
  7. 8xyz
7 0
2 years ago
Other questions:
  • How do you answer a, b and c, answers and also how you worked it out
    11·1 answer
  • Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.
    6·1 answer
  • The ___ of the ___ angle of an isosceles triangle is also the what of the base
    10·1 answer
  • Your new TV screen has a width that is 4 inches longer than its height. If the screen's diagonal measurement is 20 inches, find
    7·1 answer
  • An angle t is drawn from the center of the unit circle. Find a formula in terms of t for the straight line distance d between th
    13·1 answer
  • 845,333,129 expanded​
    8·1 answer
  • A is what percent of B?<br><br>d)<br><br>A = 8 oz, B = 1.5 lb <br>Plz help need by today
    7·1 answer
  • Wyatt invests $1200 into an account that earns 6.2% simple interest for 4 years. He does not make any other deposits or withdraw
    7·2 answers
  • How to change 7/10 to a percent
    9·1 answer
  • I need help finding the slope and what m =
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!