A rock is dropped off the edge of a cliff its distance S (in feet) from the top of the cliff after T seconds is S(T) = 16t^2. Assumme the distance from the top of the water below is 96ft.
When will the rock strike the water?
T=16t^2 -96
96=16t^2
80=t^2
4 and squareroot of 5= t
Im not sure if if i did it right because the chapter is about limits
Well, let's dive into this problem and see if we can make a splash with our answer! Your approach seems pretty solid so far. We want to find when the rock will strike the water, so we can set the distance S(T) equal to the distance from the top of the water, which is 96 feet. So, we have the equation:
S(T) = 16t^2 = 96
Now, let's solve for t. Dividing both sides by 16, we get:
t^2 = 6
Taking the square root of both sides, we find:
t = ±√6
Since time can't be negative in this case, we'll ignore the negative value. So, the rock will strike the water at approximately t = √6 seconds.
Now, let me make a joke to lighten the mood: Why did the rock go to therapy? It had some serious "fallings"!
To find when the rock will strike the water, we can set the equation equal to the distance from the top of the water below:
S(T) = 96
Substituting the equation for S(T):
16t^2 = 96
Dividing both sides by 16:
t^2 = 6
Taking the square root of both sides:
t = √6
Therefore, the rock will strike the water approximately √6 seconds after it is dropped.
To find the time at which the rock strikes the water, we need to set the distance function S(T) equal to the distance from the top of the water, which is 96 feet.
So we have the equation:
16t^2 = 96
To solve for t, we can divide both sides of the equation by 16:
t^2 = 6
Taking the square root of both sides, we get:
t = √6
Therefore, the rock will strike the water approximately √6 seconds after it is dropped off the edge of the cliff.
You need major help in algebra, not calculus. You may want to drop calculus, if the above work reflects your algebra ability. You made major errors in manipulation and solving that simple equation.
S(t)=16t^2
find t when S=96
96=16^t^2
t^2=96/16 =6
t= sqrt(6)