Question

The height of lava fountains spewed from volcanoes cannot be measured directly. Instead, their height in meters can be found using the equation

where y represents the height, g is 9.8, and t represents the falling time of the lava rocks. Find the height in meters of a lava rock that falls for 3 seconds.

Answer 1

The given equation for the height of a lava fountain is:

y = (1/2)gt^2

where y is the height in meters, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time in seconds.

To find the height of a lava rock that falls for 3 seconds, we can substitute t = 3 into the equation:

y = (1/2)(9.8 m/s^2)(3 s)^2 = (1/2)(9.8 m/s^2)(9 s^2) = 44.1 meters

Therefore, the height of a lava rock that falls for 3 seconds is approximately 44.1 meters.