Question

Niagara Falls is made up of three waterfalls. The height of the Canadian Horseshoe Falls is about 188 feet above the lower Niagara River. A log falls from the top
of Horseshoe Falls.
a. Write a function that gives the height h (in feet) of the log after t seconds. How long does it take the log to reach the river? Round your answer to the nearest
tenth

Answer 1

Answer:

• h(t) = -16t^2 +188
• 3.4 seconds

Step-by-step explanation:

The usual equation for ballistic motion is ...

  h(t) = -16t^2 +v0·t +s0

where v0 is the initial upward velocity, and s0 is the initial height above some reference point.

Here, we presume there is no initial vertical velocity, and the height is given as 188 ft above the river. Since we want the time to reach the river, we're solving ...

  h(t) = -16t^2 +188

  h(t) = 0

  -16t^2 +188 = 0

  t^2 -11.75 = 0

  t = √11.75 ≈ 3.4

It takes about 3.4 seconds for the log to reach the river.