2. a basket ball is dropped by galileo from a tall building. choose the positive y to be downward with its…

Explanation:

Step1: Identify the acceleration

The acceleration of an object in free - fall near the surface of the Earth is $a = g=9.8m/s^{2}$ (since positive $y$ is downward). So the answer to part a is $9.8m/s^{2}$.

Step2: Use the kinematic equation for distance

The kinematic equation for distance is $y = y_0+v_0t+\frac{1}{2}at^{2}$. Since $y_0 = 0$ and $v_0 = 0$, when $t = 2s$ and $a = 9.8m/s^{2}$, we have $y=\frac{1}{2}\times9.8\times2^{2}$. $y=\frac{1}{2}\times9.8\times4 = 19.6m$

Step3: Use the kinematic equation for velocity - distance

The kinematic equation $v^{2}=v_0^{2}+2a(y - y_0)$. Since $y_0 = 0$ and $v_0 = 0$, when $y = 15m$ and $a = 9.8m/s^{2}$, we have $v=\sqrt{2\times9.8\times15}$. $v=\sqrt{294}\approx17.15m/s$

Step4: Use the kinematic equation for distance - time

Using $y = y_0+v_0t+\frac{1}{2}at^{2}$ with $y_0 = 0$ and $v_0 = 0$, when $y = 25m$ and $a = 9.8m/s^{2}$, we get $25=\frac{1}{2}\times9.8\times t^{2}$. Then $t^{2}=\frac{25\times2}{9.8}$, and $t=\sqrt{\frac{50}{9.8}}\approx2.26s$

Step5: Use the kinematic equation for velocity - time

The kinematic equation $v = v_0+at$. Since $v_0 = 0$, when $v = 29.4m/s$ and $a = 9.8m/s^{2}$, we have $t=\frac{v}{a}=\frac{29.4}{9.8}=3s$

Answer:

a. $9.8m/s^{2}$ b. $19.6m$ c. $\approx17.15m/s$ d. $\approx2.26s$ e. $3s$