An arrow is shot horizontally from a cliff at 15 m/s land 30 m away. How high is the cliff?

17.2

To find the height of the cliff, we can use the kinematic equation for horizontal motion:

Distance = Velocity * Time

In this case, we know the distance the arrow traveled horizontally, but we need to find the time it took to reach that distance.

First, let's find the time it takes for the arrow to reach the horizontal distance of 30 meters. Since the arrow is shot horizontally, there is no vertical motion in the horizontal direction, so the time will be the same as if the arrow was dropped vertically from the same height. We can use the equation for vertical motion to find the time:

Vertical Distance = (1/2) * Acceleration * Time^2

Since the vertical distance is the height of the cliff, we can rewrite the equation as:

Height = (1/2) * Acceleration * Time^2

Since the arrow was shot horizontally, the initial vertical velocity (Vy) is 0 m/s. Thus, the vertical motion equation becomes:

Height = (1/2) * Acceleration * Time^2

Now, we need to find the time it takes for the arrow to reach the horizontal distance of 30 meters. We can use the horizontal distance and initial horizontal velocity (Vx) to find the time:

Distance = Velocity * Time

Since the arrow was shot horizontally, the initial horizontal velocity (Vx) is 15 m/s. Thus, the horizontal motion equation becomes:

30 m = 15 m/s * Time

Divide both sides of the equation by 15:

2 = Time

Now that we know the time is 2 seconds, we can substitute this value back into the vertical motion equation:

Height = (1/2) * Acceleration * Time^2

Height = (1/2) * 9.8 m/s^2 * (2 s)^2

Height = 4.9 m/s^2 * 4 s^2

Height = 19.6 meters

Therefore, the height of the cliff is 19.6 meters.