QuestionJune 19, 2025

An archer shoots an arrow with an initial velocity of 40m/s at an angle of 20^circ above the horizontal. How far will the arrow travel horizontally before it lands? Round all intermediate values and final answer to two decimal places __

An archer shoots an arrow with an initial velocity of 40m/s at an angle of 20^circ above the horizontal. How far will the arrow travel horizontally before it lands? Round all intermediate values and final answer to two decimal places __
An archer shoots an arrow with an initial velocity of 40m/s at an angle of 20^circ above the horizontal. How far will the arrow travel horizontally before it lands? Round all intermediate values and final answer to two decimal places __

Solution
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Answer

152.68 m Explanation 1. Calculate horizontal and vertical components of velocity Use v_{x} = v \cdot \cos(\theta) and v_{y} = v \cdot \sin(\theta). For v = 40 \, m/s and \theta = 20^{\circ}, calculate v_{x} = 40 \cdot \cos(20^{\circ}) and v_{y} = 40 \cdot \sin(20^{\circ}). 2. Calculate time of flight Use t = \frac{2 \cdot v_{y}}{g} where g = 9.81 \, m/s^2. Substitute v_{y} from Step 1 to find t. 3. Calculate horizontal distance Use d = v_{x} \cdot t. Substitute v_{x} from Step 1 and t from Step 2 to find d.

Explanation

1. Calculate horizontal and vertical components of velocity<br /> Use $v_{x} = v \cdot \cos(\theta)$ and $v_{y} = v \cdot \sin(\theta)$. For $v = 40 \, m/s$ and $\theta = 20^{\circ}$, calculate $v_{x} = 40 \cdot \cos(20^{\circ})$ and $v_{y} = 40 \cdot \sin(20^{\circ})$.<br />2. Calculate time of flight<br /> Use $t = \frac{2 \cdot v_{y}}{g}$ where $g = 9.81 \, m/s^2$. Substitute $v_{y}$ from Step 1 to find $t$.<br />3. Calculate horizontal distance<br /> Use $d = v_{x} \cdot t$. Substitute $v_{x}$ from Step 1 and $t$ from Step 2 to find $d$.
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