Final answer:
The height of the cliff from which the diver jumps horizontally can be calculated using the kinematic equation h = 0.5 × g × t². Substituting the given time t = 3.5 s and the acceleration due to gravity g = 9.81 m/s², the height is found to be approximately 60.1 meters.
Step-by-step explanation:
To calculate the height of the cliff, we must consider the vertical motion of the diver because the horizontal velocity does not affect the vertical descent. Since the diver jumps horizontally off the cliff with no initial vertical velocity, we can use the kinematic equation for vertical motion under constant acceleration due to gravity:
h = ½ g t²
Where h is the height of the cliff, g is the acceleration due to gravity (approximately 9.81 m/s²), and t is the time in seconds the diver is in the air.
Given that t = 3.5 s, we can substitute the values into the equation
h = ½ × 9.81 m/s² × (3.5 s)²
h = ½ × 9.81 m/s² × 12.25 s²
h = 0.5 × 9.81 m/s² × 12.25 s²
h ≈ 60.1 m
Therefore, the height of the cliff is approximately 60.1 meters.