Final answer:
To find when the object will hit the ground, we can solve the quadratic equation -16t²+147t+4 = 217. Using the quadratic formula, we find two solutions, t = -4.06 seconds and t = -5.19 seconds. However, since time cannot be negative in this context, we choose the positive solution, t = -4.06 seconds.
Step-by-step explanation:
To determine when the object will hit the ground, we need to solve the quadratic equation 217 = -16t²+147t+4.
First, we rearrange the equation to get it in the form ax² + bx + c = 0, where a = -16, b = 147, and c = -213.
We can then use the quadratic formula to find the values of t. Plugging in the values, we get:
t = (-b ± √(b² - 4ac)) / (2a)
Calculating the discriminant, b² - 4ac, we get 147² - 4(-16)(217) = 361
Since the discriminant is positive, we have two real solutions:
t = (-147 ± √361) / (-32)
t = (-147 ± 19) / (-32)
Therefore, the object will hit the ground at two different times: t = -130/32 ≈ -4.06 seconds and t = -166/32 ≈ -5.19 seconds. However, since time cannot be negative in this context, we only consider the positive solution. Hence, the object will hit the ground at approximately t = -4.06 seconds.