Question

A stone is thrown vertically downward from a cliff 194-m tall. During the last half second of its flight, the stone travels a distance of 43.70 m. Find the initial speed of the stone.

Answer 1

To find the initial speed of the stone, use the kinematic equation Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2. Calculate the initial velocity using the given values and solve the equation. The initial velocity of the stone is approximately 84.8 m/s.

Step-by-step explanation:

To find the initial speed of the stone, we can use the kinematic equation:

Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2

Since the stone is thrown vertically downward, the distance is equal to the height of the cliff:

Distance = 194 m

The time during the last half second of the stone's flight is given as 0.5 s, and the acceleration due to gravity is approximately 9.8 m/s^2. Substituting these values into the equation, we get:

194 m = Initial Velocity * 0.5 s + (1/2) * (9.8 m/s^2) * (0.5 s)^2

Simplifying the equation, we have:

Initial Velocity = (194 m - (1/2) * (9.8 m/s^2) * (0.5 s)^2) / (0.5 s)

Calculating the values, we find that the initial velocity of the stone is approximately 84.8 m/s.