Angel Falls in southeastern Venezuela is the highest uninterrupted waterfall in the world, dropping 979 m (3212 ft). Assume that it takes 14 s for the water to fall from the lip of the falls to the river below. If the water lands 60 m from the base of the vertical cliff, what was its horizontal speed at the top?
in real life, air resistance is considerable, and cannot be ignored.
neglecting air resistance, then time to fall
h=1/2 g t^2 solve for time t.
velocity horizontal*time=60m solve for velocity.
To determine the horizontal speed of the water at the top of Angel Falls, we can use the equation of motion:
horizontal distance = horizontal speed × time
Given:
- Vertical distance (height) of the waterfall = 979 m
- Time taken for the water to fall = 14 s
- Horizontal distance from the base of the cliff = 60 m
We need to find the horizontal speed.
First, let's calculate the vertical speed of the water at the top of the waterfall using the equation of motion:
vertical distance = vertical velocity × time + (1/2) × acceleration × time^2
Since the water falls vertically without any horizontal acceleration, the vertical velocity remains constant throughout the fall. Therefore, the equation becomes:
979 m = vertical velocity × 14 s + (1/2) × 9.8 m/s^2 × (14 s)^2
Simplifying the equation:
979 m = vertical velocity × 14 s + 686 m
Subtracting 686 m from both sides:
293 m = vertical velocity × 14 s
Dividing both sides by 14 s:
vertical velocity = 293 m ÷ 14 s
vertical velocity ≈ 20.93 m/s
Now that we have the vertical velocity, we can calculate the horizontal speed using the horizontal distance traveled:
horizontal distance = horizontal speed × time
60 m = horizontal speed × 14 s
Dividing both sides by 14 s:
horizontal speed = 60 m ÷ 14 s
horizontal speed ≈ 4.29 m/s
Therefore, the horizontal speed of the water at the top of Angel Falls is approximately 4.29 m/s.
To find the horizontal speed of the water at the top of the falls, we can use the equations of motion.
First, let's assume that there is no air resistance affecting the horizontal motion of the water. In this case, the horizontal speed remains constant throughout the motion.
We know that the horizontal distance traveled by the water is 60 meters and the time it takes to fall is 14 seconds. We can use the equation:
distance = speed × time
Therefore, the horizontal speed can be calculated as:
speed = distance / time
Plugging in the values, we get:
speed = 60 m / 14 s = 4.29 m/s
So, the horizontal speed of the water at the top of Angel Falls is approximately 4.29 meters per second.