Answer: 6.12 seconds
Explanation:
To find when the object strikes the ground, we need to find the time t when the height h(t) is equal to 0 (since the ground is at height 0). We have the equation:
h(t) = -4.9t² + 9.31t + 239.12
To find the time when the object strikes the ground, we need to find the value of t when h(t) = 0:
0 = -4.9t² + 9.31t + 239.12
This is a quadratic equation of the form at² + bt + c = 0, where a = -4.9, b = 9.31, and c = 239.12. We can solve this equation for t using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
Plugging the values of a, b, and c into the formula, we get:
t = (-(9.31) ± √((9.31)² - 4(-4.9)(239.12))) / (2(-4.9))
t = (-9.31 ± √(86.6161 + 4694.336)) / (-9.8)
t = (-9.31 ± √(4780.9521)) / (-9.8)
t ≈ (-9.31 ± 69.14) / (-9.8)
We will have two possible values for t:
t₁ ≈ (-9.31 + 69.14) / (-9.8) ≈ 6.12 (rounded to two decimal places)
t₂ ≈ (-9.31 - 69.14) / (-9.8) ≈ 8.00 (rounded to two decimal places)
Since the height function describes the motion of the ball from a platform, we can discard the negative solution as it represents an invalid time before the ball is launched. Thus, the object strikes the ground at approximately t ≈ 6.12 seconds.