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Answer :
Final answer:
The maximum height reached by the projectile is 33.61 meters.
Explanation:
To determine the maximum height reached by the projectile, we need to analyze the vertical motion of the projectile. In this case, the initial vertical velocity is given by
Vy = V * sin(θ),
where V is the initial speed of the projectile and θ is the launch angle.
Plugging in the values, we get Vy = 37.6 m/s * sin(43.3°) = 25.69 m/s.
At the maximum height, the vertical velocity will be zero. We can use the kinematic equation
Vy = V0y - g * t
where V0y is the initial vertical velocity, g is the acceleration due to gravity, and t is the time.
Solving for t, we get t = V0y / g = 25.69 m/s / 9.8 m/s^2 = 2.62 s.
Using the time at maximum height, we can find the maximum height H using the equation
H = V0y * t - 0.5 * g * t^2 =
H = (25.69 m/s * 2.62 s) - (0.5 * 9.8 m/s^2 * (2.62 s)^2) = 33.61 m.
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