Question

an object is thrown Upward at a speed of 107 ft per second by a machine from a height of 5 ft off the ground the height h of the object after T seconds can be found using the equation h=-16t² + 107t + 5. when will the height be 20 feet

Answer 1

To find the time when the height will be 20 feet, solve the equation h = -16t² + 107t + 5 by setting it equal to 20 and solving for t using the quadratic formula and we get t=0.16 s

Step-by-step explanation:

To find the time when the height will be 20 feet, we can set the equation for height equal to 20 and solve for time.

The equation is h = -16t² + 107t + 5.

Substitute 20 for h:

20 = -16t² +107t + 5

Now, rearrange the equation to set it equal to zero:

-16t² + 107t - 15 = 0

This is a quadratic equation. Use the quadratic formula to solve for t:

t = (-107 ± sqrt(107² - 4(-16)(-15)) / (2(-16))

t = (-107 ± sqrt(11449 - 960) / (-32)

t = (-107 ± sqrt(10489) / (-32)

t ≈ (-107 ± 102.42) / (-32)

There are two possible solutions for t, which are approximately:

t ≈ -5.47 s and t ≈ 0.16 s

The positive root, t ≈ 0.16 s, is the time when the height will be 20 feet.