To find the speed at which the rock was thrown horizontally, we can use the equations of motion for projectile motion.
Given: Height of the cliff (h) = 100.0 m Horizontal distance (range) (x) = 90.0 m Acceleration due to gravity (g) = 9.8 m/s²
In horizontal motion, there is no acceleration, so the horizontal component of the initial velocity (ux) remains constant throughout the motion.
The time taken (t) for the rock to reach the ground can be calculated using the equation for vertical motion:
h = (1/2) * g * t²
Substituting the known values:
100 = (1/2) * 9.8 * t²
Solving for t²:
t² = (2 * 100) / 9.8 t² = 20.408
t ≈ √20.408 t ≈ 4.52 seconds
Now, we can find the horizontal component of the initial velocity (ux) using the equation:
x = ux * t
Substituting the known values:
90 = ux * 4.52
Solving for ux:
ux = 90 / 4.52 ux ≈ 19.92 m/s
Therefore, the rock was thrown horizontally with a speed of approximately 19.92 m/s.