QuestionJune 1, 2025

A coin is thrown straight downward from the top of a building and travels -150m The final velocity of coin when it reaches the ground is -80.0m/s What was the initial velocity of the coin if we ignore air resistance? v_(i)=[?]m/s

A coin is thrown straight downward from the top of a building and travels -150m The final velocity of coin when it reaches the ground is -80.0m/s What was the initial velocity of the coin if we ignore air resistance? v_(i)=[?]m/s
A coin is thrown straight downward
from the top of a building and travels
-150m The final velocity of coin when
it reaches the ground is -80.0m/s
What was the initial velocity of the coin if we
ignore air resistance?
v_(i)=[?]m/s

Solution
4.0(363 votes)

Answer

v_i = -96.6 \, \text{m/s} Explanation 1. Identify the formula Use the kinematic equation v_f^2 = v_i^2 + 2a d to find initial velocity. 2. Substitute known values Given: v_f = -80.0 \, \text{m/s}, d = -150 \, \text{m}, a = 9.8 \, \text{m/s}^2. Substitute into the formula: (-80)^2 = v_i^2 + 2(9.8)(-150). 3. Solve for v_i Calculate: 6400 = v_i^2 - 2940. Rearrange: v_i^2 = 6400 + 2940 = 9340. Take square root: v_i = \sqrt{9340}.

Explanation

1. Identify the formula<br /> Use the kinematic equation $v_f^2 = v_i^2 + 2a d$ to find initial velocity.<br />2. Substitute known values<br /> Given: $v_f = -80.0 \, \text{m/s}$, $d = -150 \, \text{m}$, $a = 9.8 \, \text{m/s}^2$. Substitute into the formula: $(-80)^2 = v_i^2 + 2(9.8)(-150)$.<br />3. Solve for $v_i$<br /> Calculate: $6400 = v_i^2 - 2940$. Rearrange: $v_i^2 = 6400 + 2940 = 9340$. Take square root: $v_i = \sqrt{9340}$.
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