Translate the sentence into a equation six more than the product of a number and 7 equals 5

An object launched straight up at a speed of 29.4 meters per second has a height, h, in meters of h , t seconds after the object

Nostrana [21]

Answer:

h = 44.06 meters (maximum height)

the time the object takes to complete this whole path is 6 seconds, this is why the time at which the object reaches its maximum height will between 0 and 6 seconds

Step-by-step explanation:

To solve this question, we need to first recognize that this is a constant acceleration problem, specifically, it can be thought of as a projectile motion problem.

Recall, the equations of motion:

$1) v^2 - v_0^2 = 2a(s - s_0)\\2) s = v_0^2 + \frac{1}{2} at^2\\3) v = v_0 + at$

What do we already know?

$v_0 = 29.4 ms^-1$
The launch is straight up
$a = -9.81 ms^-2$ this is the gravitational acceleration $g$

$s_0 = 0 m$ , since our reference point is at s = 0, (the ground)

We can use use the Eq(1):

we know that when any object is launched up, at maximum height its velocity is going to be zero, $v = 0 ms^-2$

$v^2 - v_0^2 = 2a(s - s_0)\\0^2 - (29.4)^2 = 2(-9.81)(s- 0)\\s = 44.06 m$

this is the maximum height!

Why does t have to between zero and six?

We can answer this using a bit visualization, if you think about the second equation

$s = v_0 t - \frac{1}{2}at^2\\ s = 29.4t - 4.905t^2$

this is the equation of the whole trajectory that object makes.

and if you solve this by making $s = 0$ , you will get the times at which the object was at the ground. the times will be 0s and 5.99s.

so the amount of time the object takes to go through this whole path is 6 seconds and this why the object will only reach its maximum height in between this time interval.

hope this helps :)

5 0

3 years ago

What is the probability of drawing a face card or a 4 from a 52 card deck?

ElenaW [278]

Probability of drawing a face card or 4 is 16/52=4/13

4 0

2 years ago

Read 2 more answers

Convert the decimal into a reduce fraction.

Ivanshal [37]

Answer:

hey i dont really know, but look up calculator soup, it has a ton of different calculators and may be able to help u

Step-by-step explanation:

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7 0

2 years ago

Simplify this exponential expression:<br><br> (-49) 2/5

ioda

Answer:

I think it is 12 4/5

Step-by-step explanation:

hope this helps if not let me now

4 0

2 years ago

A rocket is launched from the top of a 99-foot cliff with an initial velocity of 122 ft/s.

Harman [31]

Remember that c is the initial height. Since we the rocket is in a 99-foot cliff, c=99. Also, we know that the velocity of the rocket is 122 ft/s; therefore v=122
Lets replace the values into the the vertical motion formula to get:
$0=-16 t^{2} +122t+99$
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
$-99=-16 t^{2} +122t+99$
$-16 t^{2} +122+198=0$

Now we can apply the quadratic formula $t= \frac{-b+or- \sqrt{ b^{2} -4ac} }{2a}$ where a=-16, b=122, and c=198
$t= \frac{-122+or- \sqrt{ 122^{2}-(4)(-16)(198) } }{(2)(-16)}$
$t= \frac{-122+ \sqrt{27556} }{-32}$ or $t= \frac{-122- \sqrt{27556} }{-32}$
$t= \frac{-122+166}{-32}$ or $t= \frac{-122-166}{-32}$
$t= \frac{-11}{8}$ or $t=9$

Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.

5 0

3 years ago

Read 2 more answers