Final answer:
The height of the cliff from which a projectile is fired horizontally with an initial speed of 30 m/s and falls to the ground after two seconds is calculated using the equation h = ½gt^2, where g is the acceleration due to gravity (9.8 m/s^2). The resulting cliff height is 19.6 meters.
Step-by-step explanation:
The question involves calculating the height of a cliff from which a projectile is fired horizontally with an initial velocity.
The projectile falls to the ground after two seconds, and we are to ignore air resistance.
To find the height, we can use the equation of motion for freely falling bodies under gravity, for which the only acceleration is due to gravity (g = 9.8 m/s2).
The equation is:
h = ½gt2
Substitute the values for g (9.8 m/s2) and t (2 seconds) to get:
h = ½ * 9.8 m/s2 * (2 s)2
Calculate to find:
h = 19.6 m
So, the height of the cliff is 19.6 meters.