Solution:
The concept is the same with Problem 2.56 .
Part A
( v y 2 ) 2 = ( v y 1 ) 2 + 2 a Δ y ( v y 2 ) 2 = ( v y 1 ) 2 + 2 a ( y 2 − y 1 ) v y 2 = ( v y 1 ) 2 + 2 a ( y 2 − y 1 ) v y 2 = − ( 0 ) 2 + 2 ( − 9.81 m/s 2 ) ( 0 m − 1.50 m ) v y 2 = − 5.42 m/s ( Answer ) \begin{align*}
\left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \Delta y \\
\left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \left( y_2 - y_1 \right) \\
v_{y_2} & = \sqrt{\left( v_{y_1} \right)^2 + 2 a \left( y_2 - y_1 \right)} \\
v_{y_2} & = - \sqrt{\left( 0 \right)^2+2\left( -9.81\ \text{m/s}^2 \right)\left( 0\ \text{m} - 1.50\ \text{m} \right)} \\
v_{y_2} & = - 5.42 \ \text{m/s} \qquad {\color{DarkOrange} \left( \text{Answer} \right)}
\end{align*} ( v y 2 ) 2 ( v y 2 ) 2 v y 2 v y 2 v y 2 = ( v y 1 ) 2 + 2 a Δ y = ( v y 1 ) 2 + 2 a ( y 2 − y 1 ) = ( v y 1 ) 2 + 2 a ( y 2 − y 1 ) = − ( 0 ) 2 + 2 ( − 9.81 m/s 2 ) ( 0 m − 1.50 m ) = − 5.42 m/s ( Answer ) Part B
( v y 2 ) 2 = ( v y 1 ) 2 + 2 a Δ y ( v y 2 ) 2 = ( v y 1 ) 2 + 2 a ( y 2 − y 1 ) ( v y 1 ) 2 = ( v y 2 ) 2 − 2 a ( y 2 − y 1 ) v y 1 = ( v y 2 ) 2 − 2 a ( y 2 − y 1 ) v y 1 = ( 0 m/s ) 2 − 2 ( − 9.81 m/s 2 ) ( 1.10 m − 0 m ) v y 1 = 4.65 m/s ( Answer ) \begin{align*}
\left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \Delta y \\
\left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \left( y_2 - y_1 \right) \\
\left( v_{y_1} \right)^2 & = \left( v_{y_2} \right)^2 - 2 a \left( y_2 - y_1 \right) \\
v_{y_1} & = \sqrt{\left( v_{y_2} \right)^2 - 2 a \left( y_2 - y_1 \right)} \\
v_{y_1} & = \sqrt{\left( 0 \ \text{m/s} \right)^2 -2\left( -9.81 \ \text{m/s}^2 \right) \left( 1.10 \ \text{m} - 0 \ \text{m} \right) }\\
v_{y_1} & = 4.65 \ \text{m/s} \qquad {\color{DarkOrange} \left( \text{Answer} \right)}
\end{align*} ( v y 2 ) 2 ( v y 2 ) 2 ( v y 1 ) 2 v y 1 v y 1 v y 1 = ( v y 1 ) 2 + 2 a Δ y = ( v y 1 ) 2 + 2 a ( y 2 − y 1 ) = ( v y 2 ) 2 − 2 a ( y 2 − y 1 ) = ( v y 2 ) 2 − 2 a ( y 2 − y 1 ) = ( 0 m/s ) 2 − 2 ( − 9.81 m/s 2 ) ( 1.10 m − 0 m ) = 4.65 m/s ( Answer ) Part C
a = Δ v Δ t a = v 2 − v 1 Δ t a = 4.65 m/s − ( − 5.42 m/s ) 3.50 × 1 0 − 3 s a = 2877 m/s 2 a = 2.88 × 1 0 3 m/s 2 ( Answer ) \begin{align*}
a & = \frac{\Delta v}{\Delta t} \\
a & = \frac{v_2-v_1}{\Delta t} \\
a & = \frac{4.65 \ \text{m/s} - \left( -5.42 \ \text{m/s} \right)}{3.50 \times 10^{-3} \ \text{s}} \\
a & = 2877 \ \text{m/s}^2 \\
a & = 2.88 \times 10^{3}\ \text{m/s}^2 \ \qquad {\color{DarkOrange} \left( \text{Answer} \right)}\\
\end{align*} a a a a a = Δ t Δ v = Δ t v 2 − v 1 = 3.50 × 1 0 − 3 s 4.65 m/s − ( − 5.42 m/s ) = 2877 m/s 2 = 2.88 × 1 0 3 m/s 2 ( Answer ) Part D
( v y 2 ) 2 = ( v y 1 ) 2 + 2 a Δ y Δ y = ( v y 2 ) 2 − ( v y 1 ) 2 2 a Δ y = ( 0 m/s ) 2 − ( − 5.42 m/s ) 2 2 ( 2.88 × 1 0 3 m/s 2 ) Δ y = − 0.00510 m Δ y = − 5.10 × 1 0 − 3 m ( Answer ) \begin{align*}
\left( v_{y_2} \right)^2 & = \left( v_{y_1} \right)^2 + 2 a \Delta y \\
\Delta y & = \frac{\left( v_{y_2} \right)^2 - \left( v_{y_1} \right)^2}{2 a} \\
\Delta y & = \frac{\left( 0 \ \text{m/s} \right)^2 - \left( -5.42 \ \text{m/s} \right)^2}{2\left( 2.88 \times 10^3 \ \text{m/s}^2 \right)}\\
\Delta y & = -0.00510 \ \text{m} \\
\Delta y & = -5.10 \times 10^{-3} \ \text{m} \ \qquad \ {\color{DarkOrange} \left( \text{Answer} \right)}\\
\end{align*} ( v y 2 ) 2 Δ y Δ y Δ y Δ y = ( v y 1 ) 2 + 2 a Δ y = 2 a ( v y 2 ) 2 − ( v y 1 ) 2 = 2 ( 2.88 × 1 0 3 m/s 2 ) ( 0 m/s ) 2 − ( − 5.42 m/s ) 2 = − 0.00510 m = − 5.10 × 1 0 − 3 m ( Answer )
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