The height of a leaf above the ground after it falls from a tree is given by the formula s(t)=-3.8t^2+47.3, where time is given in seconds and height is given in feet. When would the leaf land on the top of the person's head if the person was seated on the ground and their head was 2.7 feet above the ground?
To find when the leaf lands on the top of the person's head, we need to find the time, t, when the height of the leaf is equal to the height of the person's head.
The height of the person's head is 2.7 feet, so we can set up the equation:
s(t) = 2.7
Substituting in the formula for s(t):
-3.8t^2 + 47.3 = 2.7
Now we can solve for t. Rearranging the equation:
-3.8t^2 = 2.7 - 47.3
-3.8t^2 = -44.6
Divide both sides by -3.8:
t^2 = (-44.6) / (-3.8)
t^2 = 11.736842105263158
Taking the square root of both sides:
t = sqrt(11.736842105263158)
t ≈ 3.42
Therefore, the leaf would land on the top of the person's head approximately 3.42 seconds after it falls from the tree.
To find the time when the leaf lands on the top of the person's head, we need to determine when the height of the leaf is equal to the height of the person's head.
Given:
s(t) = -3.8t^2 + 47.3 (height of the leaf in feet)
Height of the person's head = 2.7 feet
First, let's set up the equation by equating the height of the leaf (s(t)) to the height of the person's head (2.7 feet):
-3.8t^2 + 47.3 = 2.7
Now, let's solve for t by isolating the variable t:
-3.8t^2 = 2.7 - 47.3
-3.8t^2 = -44.6
Next, divide both sides of the equation by -3.8 to isolate t:
t^2 = (-44.6) / (-3.8)
t^2 = 11.74
Now, take the square root of both sides to find t:
t = √11.74
t ≈ 3.43
Therefore, the leaf would land on the top of the person's head approximately 3.43 seconds after falling from the tree.
just solve
-3.8t^2+47.3 = 2.7
in the usual way