# Calculating the Time for a Ball to Fall from a 10. m Building ## Given Data - Height of building, \( h = 10.\,\text{m} \) - Acceleration due to gravity, \( g = 9.81\,\text{m/s}^2 \) - Initial velocity, \( v_ = \) (the ball is dropped) - Initial position, \( y_ = \) - Final position, \( y = -10.\,\text{m} \) (downward is negative) ## Step 1: Choose the Kinematic Equation Use the equation for distance under constant acceleration: \[ y = y_ + v_ t + \frac{1}{2} a t^2 \] Here, \( a = -g \) (since gravity acts downward). ## Step 2: Substitute Known Values \[ -10. = + \cdot t + \frac{1}{2} (-9.81) t^2 \] \[ -10. = -4.905\,t^2 \] ## Step 3: Solve for \( t \) Divide both sides by \(-4.905\): \[ \frac{-10.}{-4.905} = t^2 \] \[ 2.039 = t^2 \] Take the square root: \[ t = \sqrt{2.039} \] \[ t \approx 1.43\,\text{s} \] ## Final Answer **It takes approximately \( \boxed{1.43\,\text{s}} \) for the ball to hit the ground.**