The distance, d, in feet that an object falls in t seconds is modeled by the formula d=16t^2. if you dive from a height of 120 feet, how long will it take to hit the water?
Is this how you do it?
120=16t^2?
yes.
To find the time it takes for the object to hit the water, we need to set the distance equal to 120 feet and solve for t in the equation d = 16t^2.
Since d = 16t^2, we can substitute 120 for d in the equation:
120 = 16t^2
To solve for t, divide both sides of the equation by 16:
120/16 = t^2
7.5 = t^2
To find t, we take the square root of both sides of the equation:
t = √(7.5)
t ≈ 2.74 seconds
Therefore, it will take approximately 2.74 seconds for the object to hit the water.
To find out how long it will take for the object to hit the water, we need to solve the equation d = 16t^2 for t when d = 120.
The equation d = 16t^2 represents the distance an object falls in t seconds, with the constant 16 representing gravity (assuming no air resistance). In this case, the distance is given as 120 feet, so we can substitute d = 120 into the equation:
120 = 16t^2
To solve for t, we need to isolate the variable t. Let's start by dividing both sides of the equation by 16:
120/16 = t^2
Simplifying further:
7.5 = t^2
To solve for t, we need to take the square root of both sides:
√7.5 = √t^2
t ≈ √7.5
Using a calculator, we find that the square root of 7.5 is approximately 2.74 (rounded to two decimal places).
Therefore, it will take approximately 2.74 seconds for the object to hit the water when diving from a height of 120 feet.