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?
a. t > 2
b. t > 4
c. t > 8
d. t > 16
To find out when the marble is more than halfway down the ramp, we need to find when the distance traveled is more than half of the total length of the ramp.
Given that the total length of the ramp is 3,920 cm, half of that is 1,960 cm.
Therefore, we need to solve the inequality:
490t^2 > 1,960
Divide both sides by 490:
t^2 > 4
Take the square root of both sides:
t > 2
Therefore, the marble will be more than halfway down the ramp for t > 2 seconds.
The answer is:
a. t > 2.