Final answer:
The object will be 1000 ft above the ground at approximately 6.61 seconds and 940 ft above the ground at approximately 6.90 seconds. The reasonable domain for the function h is all real numbers, but the reasonable range is from 1700 ft to 1700 ft.
Step-by-step explanation:
To find when the object will be 1000 ft above the ground, we need to set the equation to h = 1000 and solve for t. Substituting h = 1000 into the equation, we have 1000 = -16t2 + 1700. Simplifying the equation, we get -16t2 + 1700 = 1000. Rearranging the equation and dividing by -16, we have t2 = (1700 - 1000)/16 = 700/16 = 43.75. Taking the square root of both sides, we get t ≈ ±6.61. Since time cannot be negative, we take the positive value, t ≈ 6.61 seconds.
To find when the object will be 940 ft above the ground, we use the same process as before. Setting the equation to h = 940, we have 940 = -16t2 + 1700. Simplifying the equation, we get -16t2 + 1700 = 940. Rearranging the equation and dividing by -16, we have t2 = (1700 - 940)/16 = 760/16 = 47.5. Taking the square root of both sides, we get t ≈ ±6.90. Again, since time cannot be negative, we take the positive value, t ≈ 6.90 seconds.
The reasonable domain for the function h is all real numbers, since time can take any value. However, the range for the function h is from the lowest point to the maximum height. Since the equation is a quadratic function with a negative coefficient for t2, the maximum height occurs at the vertex of the parabola. The vertex can be found using the formula t = -b/(2a) where a = -16 and b = 0. Plugging in these values, we get t = 0/(2(-16)) = 0. Therefore, the maximum height is achieved at t = 0 seconds. Since the initial height is 1700 ft and the maximum height is 1700 ft, the reasonable range for the function h is from 1700 ft to 1700 ft.