Answer:

In this scenario, a cannonball is fired with a horizontal velocity of 180 m/s from a cliff that is 100 m high. We need to determine the time it will take for the cannonball to reach the ground and the horizontal distance it will fall from the base of the cliff.

To solve this problem, we can analyze the horizontal and vertical motion of the cannonball separately.

Horizontal Motion:

Since the cannonball is fired horizontally, its initial vertical velocity is 0 m/s. Therefore, we only need to consider the horizontal velocity in this case. The horizontal velocity remains constant throughout the motion.

Horizontal distance (dx) = horizontal velocity * time

Given: horizontal velocity = 180 m/s

Vertical Motion:

For the vertical motion, we need to consider the effects of gravity. The cannonball experiences a constant downward acceleration due to gravity, which is approximately 9.8 m/s².

We can use the kinematic equation for vertical motion:

Vertical distance (dy) = initial vertical velocity * time + (1/2) * acceleration due to gravity * time²

Given: initial vertical velocity = 0 m/s (since the cannonball is fired horizontally)

Acceleration due to gravity = 9.8 m/s²

The cannonball will fall vertically from a height of 100 m.

At the time of impact, the vertical distance will be equal to -100 m (negative sign indicates downward direction).

Using the vertical motion equation, we can solve for time:

-100 m = 0 m/s * time + (1/2) * 9.8 m/s² * time²

Simplifying the equation:

4.9 m/s² * time² = 100 m

Dividing both sides by 4.9 m/s²:

time² = 100 m / 4.9 m/s²

time² ≈ 20.41 s²

Taking the square root of both sides to find the time:

time ≈ √20.41 s ≈ 4.52 s

Therefore, it will take approximately 4.52 seconds for the cannonball to reach the ground.

To find the horizontal distance it will fall from the base of the cliff, we can substitute the calculated time into the horizontal motion equation:

dx = 180 m/s * 4.52 s ≈ 814.4 m

Therefore, the cannonball will fall approximately 814.4 meters horizontally from the base of the cliff.

Explanation: