Question

An object is thrown upward at a speed of 109 feet per

second by a machine from a height of 10 feet off the
ground.
h(t) = - 16t² + 109t + 10.
When will the height be 143 feet?
When will the object reach the ground?

Answer 1

The object will reach the ground at approximately 6.82 seconds.The height of the object will be 143 feet at approximately 3.79 seconds.

Step-by-step explanation:

The height of the object, h(t), is given by the equation h(t) = -16t² + 109t + 10. To find the time when the height is 143 feet, we can set h(t) equal to 143 and solve for t. We can also find the time when the object reaches the ground by setting h(t) equal to 0 and solve for t.

For the first question, solving the equation -16t² + 109t + 10 = 143 gives us two possible values of t: t = 3.79 seconds and t = 0.54 seconds. Since the object is thrown upward, we take the longer solution, which is t = 3.79 seconds.

For the second question, solving the equation -16t² + 109t + 10 = 0 gives us two possible values of t: t = -0.07 seconds and t = 6.82 seconds. Since time cannot be negative, we discard the negative solution and the object reaches the ground at t = 6.82 seconds.