Question
QUESTION 15 An object is dropped and strikes the ground 1.9 seconds later. Ignore air resistance. To two signifcant figures, from what height was the object released? A. 150 m B. none of the above C. 75 m D. 9.8 m E. 18 m
Ask by Kelley Phillips. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The object was released from a height of approximately 18 meters.
Solution
We use the kinematic equation for free fall (with initial velocity zero):
\[
h = \frac{1}{2} g t^2
\]
Substitute \( g = 9.8 \, \text{m/s}^2 \) and \( t = 1.9 \, \text{s} \):
\[
h = \frac{1}{2} \times 9.8 \times (1.9)^2
\]
Calculate \( (1.9)^2 \):
\[
(1.9)^2 = 3.61
\]
Now multiply:
\[
h = 4.9 \times 3.61 \approx 17.689 \, \text{m}
\]
Rounded to two significant figures, we obtain:
\[
h \approx 18 \, \text{m}
\]
Thus, the correct answer is option E.
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Simplify this solution Beyond the Answer
To find the height from which the object was dropped, we can use the formula for free fall: \( h = \frac{1}{2} g t^2 \), where \( g \) is the acceleration due to gravity (approximately 9.8 m/s²), and \( t \) is the time the object is in free fall. Plugging in the values, we have \( h = \frac{1}{2} \cdot 9.8 \cdot (1.9)^2 \approx 17.7 \) m. Rounding to two significant figures gives us 18 m, so the answer is E. 18 m. If you’re ever doing this type of calculation, remember to double-check your units and the significant figures! One common mistake is forgetting to adjust for rounding in intermediate steps, which can lead you to the wrong answer more often than you’d think!
