10 points!! the hardest word problem about quadratic equation???pls help!!!thank u?

Question

when an object is released and falls freely, its height. h meters, above the ground after t seconds is represented by the relation h= -0.5t^2g+d, where g is the acceleration due to gravity and d is the initial height of the object before it is released. Since the strength of gravity varies from planet to planet, the value of g is specific to each planet.

suppose a rock is dropped from a height of 100 m on Mars and also on Venus.

On Mars, g=3.7 m/s^2 and on Venus, g=8.9 m/s^2.

how long does it take the rock to fall to a height of 25 m on each planet??

i really appreciate any help.

Answer 1

uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh....

Answer 2

When the question asks "how long" it means solve for time.  From the equation h = d - 0.5*g*t², solve for t:

t = √[2*(d - h)/g]

It is not a quadratic, but a simple square root.  Use the values of d, h and g given and solve for t in each case (use the positive root).

Answer 3

dang. i wish my best friend was here, she was better at this than me. i sucked horribly when i learned it last year in algebra. i'm sorry i really wish i could help

Answer 4

its actually a relatively simple problem.

you know g. (both 3.7 and 8.9)

you know h, which is 100.

you know d, which is 25.

plug in the numbers and your left with one equation, with one unknown, which is simple algebra.

Answer 5

Mars:

25 = -.5t^2(3.7) + 100

25 = -1.85t^2 + 100

-75 = -1.85t^2

75/1.85 = t^2

Take the square root of 75/1.85 and g = 6.367sec

Venus:

25 = -.5t^2(8.9) + 100

-75 = -4.45t^2

75/4.45 = t^2

t = square root of 75/4.45 = 4.105

Answer 6

im not doing your homework

Answer 7

This is a very simple problem. Lets approach it one step at a time.

The question asks how long it takes to drop to the ground, so in this case we will be solving for time, or t.

Using the provided equation, h= (-0.5t)^(2g) + d, we can plug in each given value to solve for t. Since h, g, and d are provided, simply substitute them into the equation.

You want to know how long it will take to drop to a height (h) of 25m, so substitute 25m for h.

The gravity on Mars is 3.7m/s^2 and on Venus 8.9 m/s^2, so you have the values for g.

The height they are dropped from is 100m, so d=100.

Plug in these values: 25= (-0.5t)^(2*3.7) + 100.

Simplify: -75=(-0.5t)^(7.4)

Using the law of logrithms: 7.4=(log(-75))/(log(-0.5t)).

I do not have a scientific calculator handy, but just enter these values into your calculator and you will have your answer.

Hope this helps!!!

Answer 8

what.......

Answer 9

h = -0.5t²g + d

On Mars:

g = 3.7 m/s²

h = -0.5*3.7t² + 100

h = 100 - 1.85t²

want time when h = 25

25 = 100 - 1.85t²

1.85t² = 75

t² = 75/1.85

t = 6.367 sec (3dp)

On Venus:

g = 8.9 m/s²

h = -0.5*8.9t² + 100

h = 100 - 4.45t²

want time when h = 25

25 = 100 - 4.45t²

4.45t² = 75

t² = 75/4.45

t = 4.105sec (3dp)