**Tangential and Normal Acceleration of a Thrown Stone**

**Introduction:**
When a stone is thrown horizontally, it means that the initial velocity of the stone is only in the horizontal direction and there is no initial vertical velocity. In this scenario, the stone experiences both tangential and normal acceleration. The tangential acceleration is the rate of change of the magnitude of the velocity, while the normal acceleration is the acceleration towards the center of the circular path.

**Determining the Tangential Acceleration:**
The tangential acceleration can be determined by calculating the rate of change of the magnitude of the velocity. In this case, since the stone is thrown horizontally, the initial velocity in the horizontal direction remains constant throughout the motion. Therefore, the tangential acceleration is zero.

**Determining the Normal Acceleration:**
The normal acceleration is the acceleration towards the center of the circular path. Since the stone is thrown horizontally, it does not move in a circular path initially. However, as the stone falls due to gravity, it starts to move in a parabolic path. At any point during this motion, the stone experiences a gravitational force acting vertically downwards. This force provides the necessary centripetal force to keep the stone moving in a curved path.

**Calculating the Normal Acceleration:**
To calculate the normal acceleration, we can use the formula for centripetal acceleration:
a = v^2 / r
where a is the acceleration, v is the velocity, and r is the radius of the circular path.

Since the stone is moving in a parabolic path, the radius of curvature changes continuously. However, at any given point, we can consider a small section of the path as a circular arc with a certain radius of curvature. Therefore, in this case, we can consider the radius of curvature as the vertical distance between the stone and its initial horizontal position.

Considering the stone falls under the influence of gravity, we can calculate the vertical distance traveled by the stone in 1 second using the formula:
y = (1/2)gt^2
where y is the vertical distance, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time (1 second).

Substituting the values, we have:
y = (1/2)(9.8)(1^2) = 4.9 m

Therefore, the radius of curvature is equal to the vertical distance, which is 4.9 m.

Now, we can calculate the normal acceleration using the formula:
a = v^2 / r
Substituting the given values, we have:
a = (15^2) / 4.9 ≈ 45.92 m/s^2

Hence, the normal acceleration of the stone 1 second after it begins to move is approximately 45.92 m/s^2.

**Conclusion:**
When a stone is thrown horizontally, it experiences both tangential and normal acceleration. The tangential acceleration is zero since the initial velocity in the horizontal direction remains constant. However, the stone experiences a normal acceleration towards the center of the circular path as it falls under the influence of gravity. By considering a small section of the path as a circular arc, we can calculate the normal acceleration using the formula for centripetal acceleration. The normal acceleration is found to be approximately 45.92 m/s^2.

An=gcosa=39/√13
at=gsina=2/√13(t=tangential)