A rock falls off of a bridge and hits the water 7 seconds later. How fast will the rock be traveling when it hits the water?
how long does it take to fall? 4.9t^2 = 7
its speed after time t is 9.8t
To determine the speed at which the rock hits the water, we need to consider the distance it falls and the time it takes to fall that distance.
The acceleration due to gravity, denoted as 'g', is approximately 9.8 meters per second squared (m/s^2). This means that the speed of an object falling freely under the influence of gravity increases by approximately 9.8 m/s each second.
Since the rock falls for 7 seconds, we can calculate the distance it falls using the formula for the distance traveled during free fall:
distance = (1/2) * g * time^2
Plugging in the values, we have:
distance = (1/2) * 9.8 * (7^2)
= (1/2) * 9.8 * 49
= 240.1 meters (rounded to one decimal place)
Now that we know the distance the rock falls, we can determine its speed using the formula:
speed = sqrt(2 * g * distance)
Substituting the values, we have:
speed = sqrt(2 * 9.8 * 240.1)
= sqrt(4701.96)
≈ 68.6 meters per second (m/s) (rounded to one decimal place)
Therefore, the rock will be traveling at approximately 68.6 meters per second when it hits the water.