Question

On a day when the water is flowing relatively gently, water in the Niagara River is moving horizontally at 4.5 m/sm/s before shooting over Niagara Falls. After moving over the edge, the water drops 53 mm to the water below.

a. If we ignore air resistance, how much time does it take for the water to go from the top of the falls to the bottom?
b. Express your answer to two significant figures and include the appropriate units.
c. How far does the water move horizontally during this time?
d. Express your answer to two significant figures and include the appropriate units.

Answer 1

a.3.29 m/s

b.3.3 m/s

c.14.8 m

d.15 m

Step-by-step explanation:

We are given that

Initial Horizontal speed=
`v_x=4.5 m/s`

Vertical component of initial speed=
`v_y=0`

Vertical distance=
`y=-53 m`

a.
`s=ut+(1)/(2)gt^2`

Using the formula and g is negative therefore
`g=-9.8m/s^2`

`-53=0-(1)/(2)(9.8)t^2`

`53=4.9t^2`

`t^2=(53)/(4.9) s`

`t=\sqrt{(53)/(4.9)}=3.29m/s`

b.Hundredth place is greater than 5 therefore, 1 will be added to tenth place and other digits on left side of tenth place remains same and digit on right side of tenth place replace by 0.

`t=3.3 m/s`

c.Horizontal acceleration=
`a_x=0`

`x=v_xt=4.5* 3.29=14.8 m`

d.Tenth place 8 is greater than 5 therefore, 1 will be added to unit place and other digits on left side of unit place remains same and digit on right side of unit place replace by 0.

Horizontal distance=15 m