A rock is thrown upwards (vertically) from the ground with an initial velocity of 40 feet per second. If acceleration due to gravity is -10 feet per second squared, how high will the rock go?

Well, let me just throw some humor your way for this question. Why did the rock go to the doctor? Because it couldn't stop falling! But don't worry, I'll give you a serious answer too. To find out how high the rock will go, we can use the formula:

final velocity squared = initial velocity squared + 2 * acceleration * distance traveled

In this case, we know the final velocity is 0 feet per second (since the rock stops at its highest point), the initial velocity is 40 feet per second, and the acceleration due to gravity is -10 feet per second squared. Plugging these values into the formula, we can solve for the distance traveled (or height):

0 = 40^2 + 2 * (-10) * distance

1600 = -20 * distance

distance = -1600 / -20

distance = 80

So, the rock will go up a height of 80 feet before it starts falling back down. Keep your eyes on the sky, but watch out for falling rocks!

To find the height the rock will reach, we can use the kinematic equation of motion:

\(v^2 = u^2 + 2as\),

where:
v = final velocity (0 ft/s, since the rock reaches its maximum height and then falls back down),
u = initial velocity (40 ft/s),
a = acceleration due to gravity (-10 ft/s^2), and
s = height reached by the rock.

Rearranging the equation, we get:

\(s = \frac{{v^2 - u^2}}{{2a}}\).

Substituting the given values, we have:

\(s = \frac{{0^2 - 40^2}}{{2(-10)}}\).

Evaluating the expression, we get:

\(s = \frac{{-1600}}{{-20}}\).

Simplifying, we find:

\(s = 80\) feet.

Therefore, the rock will reach a height of 80 feet.

To find the height the rock will reach, we can use the kinematic equation:

h = (v^2 - u^2) / (2a)

where:
h is the height,
v is the final velocity,
u is the initial velocity,
a is the acceleration.

In this case, the rock is thrown upwards, so the final velocity will be zero at the highest point. The initial velocity is 40 ft/s, and the acceleration due to gravity is -10 ft/s^2 because it acts in the opposite direction to the motion.

Let's plug in the values:

h = (0^2 - 40^2) / (2 * -10)
= (-1600) / (-20)
= 80 ft

Therefore, the rock will reach a height of 80 feet.

You are using the wrong units, the value of -10 is associated with metres not feet. (actually in most cases it is considered -9.8 )

I will assume you meant metres, not feet

height = -5t^2 + 40t
velocity = -10t + 40
at max height, velocity = 0
-10t+40 = 0
t= 4

height = -5(4^2) + 40(4) = 40 m

If your problem stated feet, then the equation would have been
height = -16t^2 + 40t
etc