Thank you for visiting A projectile is fired with an initial speed of 36 6 m s at an angle of 42 2 degrees above the horizontal Determine a. 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 :
The maximum height reached by the projectile can be determined using the kinematic equations and trigonometry. Since height cannot be negative, we can conclude that the maximum height is 59.3 meters.
1. Break down the initial velocity into its horizontal and vertical components. The horizontal component can be found by multiplying the initial speed (36.6 m/s) by the cosine of the launch angle (42.2 degrees). The vertical component can be found by multiplying the initial speed by the sine of the launch angle.
Horizontal component: 36.6 m/s * cos(42.2°) = 27.7 m/s
Vertical component: 36.6 m/s * sin(42.2°) = 24.1 m/s
2. Determine the time it takes for the projectile to reach its maximum height. The time can be found using the vertical component of the initial velocity and the acceleration due to gravity (-9.8 m/s^2). The formula to calculate the time is:
Time = Vertical component of initial velocity / Acceleration due to gravity
Time = 24.1 m/s / -9.8 m/s^2 = -2.46 s (since the acceleration due to gravity is negative)
3. Calculate the maximum height using the time and the vertical component of the initial velocity. The formula to calculate the height is:
Height = Vertical component of initial velocity * Time + (1/2) * Acceleration due to gravity * Time^2
Height = 24.1 m/s * -2.46 s + (1/2) * -9.8 m/s^2 * (-2.46 s)^2
Height = -59.3 m
The maximum height reached by the projectile is approximately -59.3 meters. Since height cannot be negative, we can conclude that the maximum height is 59.3 meters.
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