Thank you for visiting A rifle is aimed horizontally at a target 55 0 m away The bullet hits the target 1 60 cm below the aim point What. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
To calculate the bullet's flight time, use the projectile motion formula for the vertical component of its descent. The time for a bullet to drop 1.60 cm using gravity alone is approximately 0.057 seconds.
Explanation:
The question you've asked involves the principles of projectile motion, which is a topic within Physics. To find the bullet's flight time when it hits 1.60 cm below the aim point, we need to consider only the vertical descent because the horizontal aim is level. The only force acting on the bullet after it leaves the rifle is gravity, which causes it to fall below the aim point.
To calculate the vertical distance (Δy) traveled by the bullet using the formula Δy = 0.5 * g * t^2, where g is the acceleration due to gravity (9.81 m/s^2). Since the descent is 1.60 cm, we convert it to meters: 1.60 cm = 0.016 m. The time (t) it takes for this descent can be solved by rearranging the formula: t = sqrt((2 * Δy) / g).
Plugging in the values: t = sqrt((2 * 0.016 m) / 9.81 m/s^2) gives t ≈ 0.057 s. Therefore, the bullet's flight time before hitting the target is approximately 0.057 seconds.
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Rewritten by : Jeany
The bullet's flight time to reach the target is approximately 0.057 seconds.
Understanding the Setup
The bullet is aimed horizontally at a target that is 55.0 m away. Due to gravity, the bullet falls 1.60 cm (or 0.016 m) below the aim point by the time it reaches the target.
Key Concepts
- When a bullet is fired horizontally, its horizontal and vertical motions can be analyzed separately.
- The horizontal motion is uniform (constant speed), while the vertical motion is accelerated due to gravity.
Find Time of Flight
Formula for Vertical Motion: We use the formula for vertical displacement due to gravity:
[tex]y = \frac{1}{2} g t^2[/tex]
where:
[tex]y[/tex] is the vertical displacement (0.016 m)
[tex]g[/tex] is acceleration due to gravity (approximately 9.81 [tex]m/s^2[/tex])
[tex]t[/tex] is the time in seconds
Plug in the Values:
[tex]0.016 = \frac{1}{2} \times 9.81 \times t^2[/tex]
[tex]0.016 = 4.905 t^2[/tex]
(Multiply both sides by 2)
[tex]0.032 = 9.81 t^2[/tex]
[tex]t^2 = \frac{0.032}{9.81}[/tex]
[tex]t^2 = 0.00326[/tex]
[tex]t = \sqrt{0.00326}[/tex]
[tex]t \approx 0.057 \text{ seconds}[/tex]
