Question

a student drops a ball off the top of building and records that the ball takes 1.26s to reach the ground. determine all unknowns and answer the following questions. neglect drag. what was the balls speed just before striking the ground? m/s from what height was the ball dropped? m

Explanation:

Step1: Identify the kinematic - equation for final velocity

The ball is in free - fall, and the initial velocity $u = 0\ m/s$ (dropped), the acceleration $a = g=9.8\ m/s^{2}$, and the time $t = 1.26\ s$. The equation for final velocity $v$ is $v=u + at$.
$v=0+9.8\times1.26$

Step2: Calculate the final velocity

$v = 9.8\times1.26=12.348\ m/s$

Step3: Identify the kinematic - equation for height

The equation for the displacement $h$ (height in this case) when the initial velocity $u = 0\ m/s$ is $h=ut+\frac{1}{2}at^{2}$. Since $u = 0\ m/s$, the equation simplifies to $h=\frac{1}{2}gt^{2}$.
$h=\frac{1}{2}\times9.8\times(1.26)^{2}$

Step4: Calculate the height

$h = 4.9\times1.5876 = 7.77924\ m$

Answer:

The ball's speed just before striking the ground is $12.348\ m/s$.
The height from which the ball was dropped is $7.77924\ m$.