Question

1. willie robertson shoots horizontally at a duck from a height of 6m. if the initial velocity of the bullet is 95 m/s.

picture:
a. find the time it takes for the bullet to hit the ground.
formula:
plug in numbers:
answer:
b. find the horizontal distance traveled during that time... assuming he missed the duck.
formula:
plug in numbers:
answer:
c. what is the final vertical velocity?
formula:
plug in numbers:
answer:

Explanation:

a. Find the time it takes for the bullet to hit the ground

Step1: 垂直方向運動公式

垂直方向初速度\(v_{0y}=0\)，根據自由落體位移公式\(y = v_{0y}t+\frac{1}{2}gt^{2}\)，可化為\(y=\frac{1}{2}gt^{2}\)（\(y = 6m\)，\(g = 9.8m/s^{2}\)）。

Step2: 求解時間\(t\)

由\(y=\frac{1}{2}gt^{2}\)，可得\(t=\sqrt{\frac{2y}{g}}\)，代入\(y = 6m\)，\(g = 9.8m/s^{2}\)，\(t=\sqrt{\frac{2\times6}{9.8}}\approx1.11s\)。

Step1: 水平方向運動公式

水平方向做勻速直線運動，公式\(x = v_{0x}t\)（\(v_{0x}=95m/s\)，\(t\approx1.11s\)）。

Step2: 計算水平距離\(x\)

代入數值\(x = 95\times1.11 = 105.45m\)。

Step1: 垂直方向速度公式

根據\(v_{y}=v_{0y}+gt\)（\(v_{0y}=0\)，\(g = 9.8m/s^{2}\)，\(t\approx1.11s\)）。

Step2: 計算最終垂直速度\(v_{y}\)

代入得\(v_{y}=0 + 9.8\times1.11=10.88m/s\)。

Answer:

\(t\approx1.11s\)

b. Find the horizontal distance traveled during that time