Question

The quadratic equation y equals short dash 16 t squared plus 64 t plus 2 represents the height of a projectile, y, in feet, at a particular time, t, in seconds. for what interval or intervals of time will the projectile be below 50 feet?

a. 0b. .5c. 2d. 3e. 0f. 1.5

Answer 1

The projectile represented by the equation y = -16t^2 + 64t + 2 will be below 50 feet between 1 second and 3 seconds after launch, based on the solutions to the modified equation t^2 - 4t + 3 = 0.

Step-by-step explanation:

The quadratic equation given in the question: y = -16t2 + 64t + 2, represents the height (y) of a projectile at a given time (t). To find out the interval(s) of time when the projectile will be below 50 feet, we set the quadratic equation equal to 50 and solve for t:

50 = -16t2 + 64t + 2.

Rearrange the equation to bring it to standard quadratic form:

-16t2 + 64t + 2 - 50 = 0

-16t2 + 64t - 48 = 0

Dividing the whole equation by -16 we get:

t2 - 4t + 3 = 0

The solutions for this equation are the times when the projectile is exactly 50 feet in the air. The interval(s) we are looking for will be between these two times. Using the quadratic formula or factoring, we find that the roots of this equation are t = 1 and t = 3. This means that the projectile will be below 50 feet between 1 second after launch and 3 seconds after launch.