Question

An acrobat is on a platform that is 25 feet in the air. She jumps down in the initial velocity of 4 feet/seconds . Write the quadratic function to represent the height h of the acrobat t seconds after the jump. If a safety nets place 5 feet above the ground how long will it take for her to land safely on the net ?

Answer 1

a) h(t) = -16t²+ 4t + 25

b) Therefore it would take her 1.25 seconds to land safely in the net.

Explanation:

The equation to be used is given as

h(t) = –gt²+ vt + S(t)

where g = force of gravity and because our question is in feet's = 16

V= Initial velocity

h = height

S = distance

a) The quadratic function for the above question

Using the formula

v = Initial velocity in the question = 4ft/s

S(t) = 25ft in the air

Hence the Quadratic function is

h(t) = –gt²+ vt + S(t)

h(t) = -16t²+ 4t + 25

b) If the safety net is placed 5 feet above the ground, how long will it take her to land safely in the net?

We are to find the time(t)

We can calculate this by using the quadratic function we derived in question (a)

The quadratic function is

h(t) = -16t²+ 4t + 25

Where, the height (h) = 5 feet above the ground

5= -16t² + 4t + 25

-16t² + 4t + 25 -5 = 0

-16t² + 4t + 20 = 0

Using the quadratic equation formula of

x = -b ± √b² -4ac /2a

where the quadratic equation =

ax² + bx + c = 0

a = -16 , b = 4 , c = 20

x = -16 ± √4² - 4×-16×20 / 2×-16

x = -1 or ,1.25

Therefore it would take her 1.25 seconds to land safely in the net