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Answer :
The speed of the projectile 2.00 seconds after firing is approximately [tex]\( 28.42 \, \text{m/s} \)."[/tex]
The initial velocity can be broken down into horizontal and vertical components:
Given that [tex]\( v_0 = 37.1 \, \text{m/s} \) and \( \theta = 41.2^\circ \),[/tex] we can calculate the components:
[tex]\( v_{0x} = v_0 \cos(\theta) = 37.1 \, \text{m/s} \cdot \cos(41.2^\circ) \)[/tex]
[tex]\( v_{0y} = v_0 \sin(\theta) = 37.1 \, \text{m/s} \cdot \sin(41.2^\circ) \)[/tex]
The horizontal component of the velocity remains constant over time because there is no air resistance or other forces acting horizontally. Therefore, after 2.00 seconds, the horizontal velocity [tex]\( v_x \)[/tex] is the same as [tex]\( v_{0x} \).[/tex]
[tex]\( v_y = 24.30 \, \text{m/s} - 9.81 \, \text{m/s}^2 \cdot 2.00 \, \text{s} \approx 24.30 \, \text{m/s} - 19.62 \, \text{m/s} \approx 4.68 \, \text{m/s} \)[/tex]
[tex]\( v = \sqrt{(28.02 \, \text{m/s})^2 + (4.68 \, \text{m/s})^2} \approx \sqrt{785.65 \, \text{m}^2/\text{s}^2 + 21.91 \, \text{m}^2/\text{s}^2} \approx \sqrt{807.56 \, \text{m}^2/\text{s}^2} \approx 28.42 \, \text{m/s} \)[/tex]
Therefore, the speed of the projectile 2.00 seconds after firing is approximately [tex]\( 28.42 \, \text{m/s} \)."[/tex]
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Final answer:
To find the speed of a projectile 2.00 s after firing, we can use the equations of projectile motion.
Explanation:
To determine the speed of the projectile 2.00 s after firing, we can use the equations of projectile motion. Since the motion is in two dimensions, we can separate it into horizontal and vertical components. The horizontal velocity remains constant, so we can use the equation:
vx = v0 * cos(θ)
where vx is the horizontal velocity, v0 is the initial velocity, and θ is the angle of projection.
The vertical velocity changes due to gravity, so we can use the equation:
vy = v0 * sin(θ) - g * t
where vy is the vertical velocity, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time.
Using these equations, we can find the speed of the projectile 2.00 s after firing.
Learn more about Projectile motion here:
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