a marble is rolled down a ramp. The distance it travels is described by the formula d=490T^2 where d is the distance in centimeters that the marble rolls in t seconds. If the marble is released at the top of a ramp that is 3,920 cm long for what time period will the marble be more than halfway down the ramp?

Question

a marble is rolled down a ramp. The distance it travels is described by the formula d=490T^2 where d is the distance in centimeters that the marble rolls in t seconds. If the marble is released at the top of a ramp that is 3,920 cm long for what time period will the marble be more than halfway down the ramp?

Answer 1

AAAaannndd the bot gets it wrong yet again!

no, it reaches the halfway point in 2 seconds.
But it will not take another 2 seconds to get to the bottom
To find how long the whole trip takers
490t^2 = 3920
t^2 = 8
so it is more than halfway down the ramp for
√8 - 2 = 0.828 seconds

Answer 2

To find the time period for which the marble will be more than halfway down the ramp, we need to determine when the distance traveled by the marble is greater than half the length of the ramp.

Given:
d = 490T^2 (distance in centimeters)
Length of the ramp = 3,920 cm

Let's calculate the halfway point of the ramp:

Halfway point = 1/2 * Length of the ramp
Halfway point = 1/2 * 3,920 cm
Halfway point = 1,960 cm

Now, we can set up the equation and solve for T:

d = 490T^2
1,960 = 490T^2

Divide both sides of the equation by 490:

1,960/490 = (490T^2)/490
4 = T^2

Take the square root of both sides:

√4 = √T^2
2 = T

Therefore, the marble will be more than halfway down the ramp for a time period of 2 seconds.

Answer 3

To find the time period for which the marble will be more than halfway down the ramp, we need to determine the distance traveled by the marble when it is halfway down the ramp.

Given that the ramp is 3,920 cm long, the halfway point would be at a distance of 3,920/2 = 1,960 cm.

Now, let's substitute this distance (d) into the equation d = 490T^2 and solve for T.

1,960 = 490T^2

Divide both sides by 490:

1,960/490 = T^2

4 = T^2

Take the square root of both sides:

√4 = √T^2

T = ±2

Since time cannot be negative, we can disregard the negative value.

Therefore, the marble will be more than halfway down the ramp between 2 seconds and 0 seconds (when it is released).

Answer 4

First, we need to figure out what "halfway down the ramp" means. Since the ramp is 3,920 cm long, halfway down would be 1,960 cm.

We can set up an equation to solve for the time it takes the marble to travel 1,960 cm:

1,960 = 490T^2

Dividing both sides by 490 gives us:

4 = T^2

Taking the square root of both sides gives us:

T = 2 seconds

So the marble will be more than halfway down the ramp for 2 seconds.