A bird sitting 16 feet above the ground in an apple tree dislodges an apple. After how many seconds does the apple land on the ground?
my text book gives this equation: h = -16t^2 + vt + s (t = secs, v= vertical velocity, s = initial height)
so i wrote: h = -16t^2 + vt 16
I'm not sure where to go from here.
initial velocity v is zero - it just fell
initial height is 16 feet, so
h = -16t^2 + 16
So, you want to find t when h=0 (apple hits the ground)
-16t^2 + 16 = 0
-16 (t^2-1) = 0
-16(t+1)(t-1) = 0
So, the apple's height is zero when t=1; that is, one second after being dislodged from the tree.
So, what's with the t = -1 solution?
It just means that had the apple been tossed up from the ground, instead of starting from the tree, its launch would have been one second before it had been dislodged.
Thank you, Steve.
I'm workin on the same stuff.. lol
Thanks
To find out after how many seconds the apple will land on the ground, you need to solve the given equation for the time, t. Here's the correct equation for the situation:
h = -16t^2 + vt + s
Where:
h = height of the apple above the ground at any given time (in feet)
t = time in seconds
v = vertical velocity (downward) of the apple (in feet/second)
s = initial height of the apple above the ground (in feet)
In this case, you're given the following information:
s = 16 feet (initial height above the ground)
v = ? (vertical velocity, which we need to determine)
Since the bird dislodged the apple, we can assume that the initial velocity is 0 (the apple starts from rest). Therefore, v = 0.
Now, substitute the values into the equation:
h = -16t^2 + 0t + 16
Simplifying this equation:
h = -16t^2 + 16
We want to find when the apple lands on the ground, so the height (h) would be equal to 0 (since the ground is at 0 feet). Hence, we rewrite the equation as:
0 = -16t^2 + 16
Now, to solve for t, we can proceed as follows:
-16t^2 + 16 = 0
Divide both sides by -16 to simplify the equation:
t^2 - 1 = 0
Rearrange the equation:
t^2 = 1
Take the square root of both sides to isolate t:
t = ±√1
However, since time cannot be negative in this context, we discard the negative solution. Therefore, the only valid solution is:
t = √1
Finally, we find:
t = 1 second
So, the apple will land on the ground after 1 second.