The height h(t) measured in feet of an object dropped by an astronaut on the moon can be approximated by h(t) = h0 (0 on the bottom) - 2.7t^2, where h0 is the height from which the object was dropped. About how long would it take an object to fall to the moon (h = 0) if it were dropped by an astronaut from a height of 6 feet?
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Which expressions would complete this equation so that it has one solution?
4(2x – 3) – 4x =
Choose exactly two answers that are correct.
A.
4x – 12
B.
3x – 4
C.
3(2x – 6)
D.
4(x – 5)
C and B
To find out how long it would take for the object to fall to the moon, we need to set the height equation h(t) equal to zero and solve for the time t.
Given:
h(t) = h0 - 2.7t^2
h(t) = 0 (since the object has fallen to the moon, h = 0)
h0 = 6 feet
Substituting the values into the equation:
0 = 6 - 2.7t^2
Rearranging the equation:
2.7t^2 = 6
Dividing both sides by 2.7:
t^2 = 6/2.7
Simplifying:
t^2 = 2.222...
To solve for t, we need to take the square root of both sides:
t ≈ √2.222...
Using a calculator, we find:
t ≈ 1.49 seconds
Therefore, it would take approximately 1.49 seconds for the object to fall to the moon if it were dropped by an astronaut from a height of 6 feet.