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217 = -16t²+147t+4 when will the object hit the ground

User Lookashc
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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.

User Kadri
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