The equation of the projectile is y=20x−54x2 m.𝑦=20𝑥-54𝑥2 m. The horizontal range is
Question
The equation of the projectile is y=20x−54x2 m.𝑦=20𝑥-54𝑥2 m. The horizontal range is
Solution
The horizontal range of a projectile can be found using the equation of the projectile's trajectory. The equation given is y = 20x - 54x^2.
The horizontal range, R, is the x-coordinate where the projectile hits the ground, i.e., when y = 0.
So, we set y = 0 in the equation and solve for x:
0 = 20x - 54x^2 0 = x(20 - 54x)
Setting each factor equal to zero gives the solutions:
x = 0 or 20 - 54x = 0
The first solution, x = 0, corresponds to the starting point of the projectile. The second solution gives the horizontal range:
20 - 54x = 0 54x = 20 x = 20/54 x = 0.37 m
So, the horizontal range of the projectile is 0.37 meters.
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