Projectile Motion: Finding Firing Angles and Time of Flight

Math Problem Statement

Gambar diatas menunjukkan pandangan dari sebuah senapan yang telah 'dih arahkan' untuk mengenai target pada jarak 91,4 meter. Jika kecepatan peluru adalah v₀ = 427 m/s. a. Berapakah dua sudut yang mungkin, yaitu sudut θ₁ dan θ₂, antara laras senapan dan garis horizontal sehingga peluru dapat mengenai target? b. Berapakah waktu yang dibutuhkan peluru untuk mencapai target, dengan menggunakan 2 sudut tersebut?

Solution

The problem depicted involves a projectile motion scenario, where a bullet is fired from a rifle at an initial speed $v_0 = 427 \, \text{m/s}$ to hit a target located 91.4 meters away. The task is to determine the angles $\theta_1$ and $\theta_2$ at which the bullet should be fired to reach the target, and

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Math Problem Analysis

Mathematical Concepts

Projectile Motion
Trigonometry
Kinematics

Formulas

Range formula: R = (v₀² * sin(2θ)) / g
Time of flight: t = (2 * v₀ * sin(θ)) / g
Trigonometric identity: 2 sin θ cos θ = sin(2θ)

Theorems

Kinematic Equations of Motion
Trigonometric Identities

Suitable Grade Level

College Level (Physics/Engineering)

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