Final answer:
With the fall time of 2 seconds, the cliff height is calculated to be 19.6 meters.
Step-by-step explanation:
To calculate the height of the cliff from where the projectile was shot horizontally, we will use the kinematic equation for vertical motion. Since the horizontal motion does not affect the vertical motion in projectile motion, we can consider these separately. The vertical motion is affected by gravity alone because the projectile starts with a horizontal velocity, so there is no initial vertical velocity component.
We use the formula s = ut + 1/2 at^2, where s is the displacement (height of the cliff in this case), u is the initial velocity (which is 0 m/s since it is shot horizontally), a is the acceleration due to gravity (9.8 m/s^2), and t is the time taken to fall (2 seconds in this case). Plugging in the values, we get:
s = 0 m/s * 2 s + 1/2 * 9.8 m/s^2 * (2 s)^2
s = 0 + 1/2 * 9.8 m/s^2 * 4 s^2
s = 19.6 m
Therefore, the height of the cliff is 19.6 meters.