The distance, d, an object falls after t seconds is given by the equation
d=-1/2(9.8)t^2
If t^2=83sec^2 then what is a good estimate for t?
To find a good estimate for t, we can start by substituting the given value for t^2 into the equation and solve for t.
Given:
t^2 = 83 sec^2
d = -1/2(9.8)t^2
Substituting t^2 = 83 sec^2 into the equation:
d = -1/2(9.8)(83 sec^2)
Now, let's simplify the equation:
d = (-1/2)(9.8)(83 sec^2)
We can continue by multiplying the numbers:
d = - 4059.9 sec^2
Since the outcome is negative, it indicates that the object is falling downwards.
To estimate t, we can rearrange the equation to solve for t^2:
t^2 = -2d / (9.8)
Plugging in the value for d, we get:
t^2 = -2(-4059.9) / (9.8)
Simplifying:
t^2 = 829.59 / 9.8
t^2 = 84.69
To find t, we take the square root of both sides:
t = √(84.69)
Calculating the square root:
t ≈ 9.20 seconds
Therefore, a good estimate for t is approximately 9.20 seconds.