Question

A ball is thrown straight up from the top of a building that is 400 ft high with an initial velocity of 64 ft/s. The height of the object can be modeled by the equation s(t) = -16t2 + 64t + 400. Determine the time(s) the ball is higher than the building. Write your answer in interval notation. Then in two or more complete sentence, explain your solution method.

Answer 1

Answer:

The time(s) the ball is higher than the building: Interval (0,4)

Step-by-step explanation:

s(t)=-16t^2+64t+400

Determine the time(s) the ball is higher than the building:

s(t)>400

-16t^2+64t+400>400

Subtracting 400 both sides on the inequality:

-16t^2+64t+400-400>400-400

-16t^2+64t>0

Multiplying the inequality by -1:

(-1)(-16t^2+64t>0)

16t^2-64t<0

Fatorizing: Comon factor 16t:

16t(16t^2/16t-64t/16t)<0

16t(t-4)<0

t is greater than zero:

t>0→t-4<0→t-4+4<0+4→t<4

Then t>0 ant t<4:

Solution = (0, Infinite) ∩ (-Infinite, 4)

Solution = (0,4)