Final answer:
To calculate the distance the object lands from the cliff's edge, first find the time it takes to fall 74 meters, then multiply the horizontal velocity by this time. With a fall time of approximately 3.86 seconds and a horizontal velocity of 36 m/s, the object will land about 138.96 meters from the edge.
Step-by-step explanation:
To determine how far from the cliff's edge the object will land, we must calculate the time it takes for the object to fall 74 meters and then use this time to find the horizontal distance traveled. Since the object is launched horizontally, its initial vertical velocity is 0 m/s. The time (t) it takes to fall can be calculated using the equation for the vertical motion under constant acceleration (acceleration due to gravity):
d = ½ g t^2
Where d is the vertical distance (74 meters), and g is the acceleration due to gravity (-10 m/s^2). Solving for t gives:
t = sqrt(2 * d / -g)
t = sqrt(2 * 74 m / 10 m/s^2)
t ≈ 3.86 s (time to fall
Now, we can use the horizontal velocity (36 m/s) to find the horizontal distance (x) traveled during the time t. The horizontal motion is described by
x = v * t
Where v is the horizontal velocity. So the distance from the cliff's edge will be:
x = 36 m/s * 3.86 s
x ≈ 138.96 m
Therefore, the object will land approximately 138.96 meters from the cliff's edge.