QuestionJune 20, 2025

A rock is thrown upward with a velocity, of 18 meters per second from the top of a 27 meter high cliff,and it misses the cliff on the way back down. When will the rock be 2 meters from ground level? Round your answer to two decimal places. Gravity Formula

A rock is thrown upward with a velocity, of 18 meters per second from the top of a 27 meter high cliff,and it misses the cliff on the way back down. When will the rock be 2 meters from ground level? Round your answer to two decimal places. Gravity Formula
A rock is thrown upward with a velocity, of 18 meters per second from the top of a 27 meter high cliff,and it misses the cliff on the way back down. When will the rock be 2 meters from ground level? Round your answer to two decimal places. Gravity Formula

Solution
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Answer

The rock will be 2 meters from ground level at approximately 0.31 seconds and 16.39 seconds. Explanation 1. Write the equation of motion Use the formula for vertical motion: h(t) = h_0 + v_0 t - \frac{1}{2} g t^2, where h_0 = 27 m, v_0 = 18 m/s, and g = 9.8 m/s². 2. Set up the equation for height Set h(t) = 2 m: 2 = 27 + 18t - \frac{1}{2} \times 9.8 \times t^2. 3. Simplify the quadratic equation Rearrange to form 0 = -4.9t^2 + 18t + 25. 4. Solve the quadratic equation Use the quadratic formula: t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} with a = -4.9, b = 18, c = -25. 5. Calculate the discriminant Compute \Delta = b^2 - 4ac = 18^2 - 4 \times (-4.9) \times (-25). 6. Find the roots Calculate t = \frac{-18 \pm \sqrt{\Delta}}{2 \times -4.9}.

Explanation

1. Write the equation of motion<br /> Use the formula for vertical motion: $h(t) = h_0 + v_0 t - \frac{1}{2} g t^2$, where $h_0 = 27$ m, $v_0 = 18$ m/s, and $g = 9.8$ m/s².<br /><br />2. Set up the equation for height<br /> Set $h(t) = 2$ m: $2 = 27 + 18t - \frac{1}{2} \times 9.8 \times t^2$.<br /><br />3. Simplify the quadratic equation<br /> Rearrange to form $0 = -4.9t^2 + 18t + 25$.<br /><br />4. Solve the quadratic equation<br /> Use the quadratic formula: $t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = -4.9$, $b = 18$, $c = -25$.<br /><br />5. Calculate the discriminant<br /> Compute $\Delta = b^2 - 4ac = 18^2 - 4 \times (-4.9) \times (-25)$.<br /><br />6. Find the roots<br /> Calculate $t = \frac{-18 \pm \sqrt{\Delta}}{2 \times -4.9}$.
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