A stone is dropped from a building 50 m high. Its acceleration at any time, t, can be approximated by the equation a = -10. How long does it take for the stone to hit the ground at the foot of the building?

Answer: 3.16 s

correct

How do you do the Q?

To find the time it takes for the stone to hit the ground, we can use kinematic equations of motion. The equation that relates distance, initial velocity, time, and acceleration is:

\(s = ut + \frac{1}{2}at^2\)

In this case, the stone is dropped, so its initial velocity is 0 m/s. The distance, \(s\), is the height of the building, which is 50 m. The acceleration, \(a\), is given as -10 m/s^2. By substituting these values into the equation, we can solve for time, \(t\).

\(50 = 0t + \frac{1}{2} (-10) t^2\)

Simplifying the equation:

\(50 = -5t^2\)

To solve for \(t\), divide both sides of the equation by -5:

\(-10 = t^2\)

Now, take the square root of both sides to solve for \(t\):

\(t = \sqrt{-10}\)

However, we are dealing with time, which cannot be negative in this context. So, we take the absolute value of the square root to get the positive value:

\(t = \sqrt{10}\)

Calculating the value of \(t\) using a calculator, we find that \(t\) is approximately equal to 3.16 seconds.