Question

A group of employees is stranded on top of a 120 feet building because a fire occurred. Your goal is to throw a rope from a 60 feet building to the rooftop of the building using the catapult so that the employees could use it to go down to the other building. The height of the rope as it reaches the building is described by the equation -16t2 + 64t + 60 = 120. The employees need to know how long they will wait before grabbing the rope and tie on a post. How long will it take for the rope to reach the top of the building?

Paki solve gamit quadratic formula sino makasagot i mamark ko ng brainlinest

Answer 1

Explanation:

-16t² + 64t + 60 = 120

this is a quadratic equation, and its points of f(t) = 0 can be calculated. there are usual 2 such solutions for a quadratic equation.

so, we need to bring it to a form that ends in "= 0".

-16t² + 64t - 60 = 0

that is also the same as

-4t² + 16t - 15 = 0

the formula for the solutions of such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = -4

b = 16

c = -15

so,

t = (-16 ± sqrt(256 - 4×-4×-15))/(2×-4) =

= (-16 ± sqrt(256 - 240))/-8 =

= (-16 ± sqrt(16))/-8 = (-16 ± 4)/-8

t1 = (-16 + 4)/-8 = -12/-8 = 3/2

t2 = (-16 - 4)/-8 = -20/-8 = 5/2

so, it depends on what the unit of time t is. let's assume seconds.

therefore, the rope will reach the top of the building while going up after 3/2 = 1 1/2 = 1.5 seconds.

and then, as the shot rope makes a curve and comes back down again (that is why we have 2 solutions : the rope will reach the height of 120ft during its flight path twice : once while still going up, and once when coming back down again) it will be at the height of the top of the building after 5/2 = 2 1/2 = 2.5 seconds.

so, it depends if the people there can grab it at the first chance, and if the path of the rope would allow them to grab it also again on its way back down. this we don't know.

I therefore guess, that your teacher is aiming for the first solution.