Question - Solving for Acceleration Due to Gravity in Physics Problem
Solution:
The image shows a physics problem that reads:"If a ball is dropped and attains a velocity of 29.4 m/s in 3.00 s, what is the acceleration due to gravity?"To solve for the acceleration due to gravity, we can use the kinematic equation that relates initial velocity (v_i), final velocity (v_f), acceleration (a), and time (t):\[ v_f = v_i + at \]For an object that is dropped, the initial velocity is zero ($$ v_i = 0 $$), so the equation simplifies to:\[ v_f = at \]We can now solve for acceleration (a) using the final velocity (v_f) and time (t) provided:\[ a = \frac{v_f}{t} \]Plugging in the given values:\[ a = \frac{29.4 \text{ m/s}}{3.00 \text{ s}} \]\[ a = 9.8 \text{ m/s}^2 \]So, the acceleration due to gravity is $$ 9.8 \text{ m/s}^2 $$, which is consistent with the average acceleration due to gravity on Earth.
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