# Projectile Motion - Niagra Falls

• crono_
In summary, the question asks at what vertical distance below the edge of Niagara Falls does the velocity vector of water point downward at a 75° angle below the horizontal, given that the water has a horizontal speed of 2.7 m/s just before it falls. Using Newton's laws of motion, we can find the vertical and horizontal velocities of the water molecule falling off the waterfall. Using the equation tan-1 = (vy / vx) = 75 degrees, we can determine the vertical velocity to be 10.0765 m/s. Then, using the formula vfy = voy + at, we can solve for t and find it to be 1.0282 seconds. Finally, using the equation y = 1
crono_

## Homework Statement

Suppose the water at the top of Niagara Falls has a horizontal speed of 2.7 m/s just before it cascades over the edge of the falls. At what vertical distance below the edge does the velocity vector of the water point downward at a 75° angle below the horizontal?

x direction

a = 0 m/s

v0x = 2.7 m/s

vfx= 2.7 m/s

x = ?

y direction

ay = -9.80 m/s2

v0y = 0 m/s

vfy = ?

y = ?

Other Info

Angle = 75 degrees below horizontal

t = ?

## Homework Equations

Newton's laws of motion...but I'm not exactly sure which ones as it appears there are two variables missing from each one.

## The Attempt at a Solution

I'm studying for my final this Friday. This question plagued me at the beginning of the term, I never got it. The class moved on, and so did I. But I'm looking at it again and am determined to get it, but am still drawing a blank.

I'd like to find t as that would help significantly, but each equation that I've considered with it has another unknown variable as well.

Kind of flustered...

Imagine a water molecule falling off the edge of the waterfall. What's its vertical speed at time t? What's its horizontal speed? How are the vertical & horizontal speeds related to the 75 degrees?

If you do it correctly, you WILL get t.

tan-1 = (vy / vx) = 75 degrees

Wait...

vy / vx = tan 75

vy = tan 75 (vx)

vy = 10.0765 m/s

vfy = voy + at

vfy - voy / a = t

t = 1.0282 s

y = 1/2 (vfy + voy) t

y = 1/2 (10.0765 m/s + 0 m/s) 1.0282 s

y = 5.18 m ----> 5.2 m with sig figs

Hrm...interesting....

## What is projectile motion?

Projectile motion is the motion of an object through the air that is affected only by gravity and air resistance.

## How is projectile motion related to Niagra Falls?

Niagra Falls is a perfect example of projectile motion because the water from the falls follows a parabolic path through the air before hitting the ground.

## What factors affect projectile motion at Niagra Falls?

The factors that affect projectile motion at Niagra Falls include the initial velocity of the water, the angle at which it is released, and the force of gravity.

## How does air resistance impact projectile motion at Niagra Falls?

Air resistance can slightly alter the trajectory of the water at Niagra Falls, but because of the large mass of the water and the short time it is in the air, the impact is minimal.

## What is the formula for calculating the trajectory of a projectile at Niagra Falls?

The formula for calculating the trajectory of a projectile at Niagra Falls is y = y0 + xtanθ - gx^2 / (2(v0cosθ)^2), where y is the height, y0 is the initial height, x is the horizontal distance, θ is the angle, v0 is the initial velocity, and g is the acceleration due to gravity.

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