Daffy Duck Equation

Question

Daffy Duck shoots an arrow up into the air with an initial vertical velocity of 104 ft/sec. The arrow was 6 feet above the ground when released. Answer the following questions. Round answers to the nearest hundredth.

hint The formula is h=-16t2+v0t+h0

I need to find How long does it take the arrow to reach its maximum height?

What is the maximum height of the arrow?

What is the height of the arrow after 2 seconds?

When will the arrow be 100 feet above the ground?

When will the arrow strike the ground?

Answer 1

3 1/4 seconds to reach max height = 175 feet

in 2 seconds it reaches 146 feet

it reaches 100 feet at 0.8 seconds and 7.3 seconds approximately rounded to one decimal

it hits the ground at 7.8125 seconds

take the derivative and set equal to zero and solve for t at max height

-32t + 104 = 0, t = 104/32 = 3.25 seconds

plug that into the original equation to solve for max height of 175 feet

h(3.25) = 175

h(2) plug 2 into the original equaton to get h=146

h(t) = 100 = -16t^2 + 104t + 6

solve for t = about 0.8 and 7.3 as it reaches 100 on the way up and then back down

0 = h(t) = -16t^2 + 104t + 6, solve for t = 7.8125 seconds when it hits the ground, when h=0