Final answer:
To calculate the initial velocity of the rock, you can use the equations of motion. First, find the time it takes for the rock to fall from the top of the cliff to the point where it lands. Then, use the equation for horizontal motion to solve for the initial velocity of the rock. The rock was thrown with an approximate velocity of 9.93 m/s.
Step-by-step explanation:
To calculate the initial velocity of the rock, we can use the equations of motion.
First, we need to find the time it takes for the rock to fall from the top of the cliff to the point where it lands.
Using the equation y = vit + 0.5gt2, where y is the height of the cliff (90m), vi is the initial vertical velocity (0 m/s), g is the acceleration due to gravity (9.8 m/s2), and t is the time, we can solve for t:
90 = 0*t + 0.5*9.8*t2
Simplifying, we get:
4.9t2 = 90
t2 = 90/4.9
t = sqrt(90/4.9) ≈ 3.02s
Next, we can use the equation x = vixt, where x is the horizontal distance travelled (30m), vix is the initial horizontal velocity, and t is the time. Since the rock is thrown horizontally, vix is equal to the initial velocity of the rock.
30 = v*t
30 = v*3.02
v = 30/3.02 ≈ 9.93 m/s
Therefore, the rock was thrown with an approximate velocity of 9.93 m/s.