Answer :
Final answer:
To find the distance x and y, break the initial velocity into horizontal and vertical components. The stone hits the cliff at x = 115.5 m and y = 47.53 m. The speed of the stone at impact is 42.0 m/s.
Explanation:
To find the distance x and y, we can break the initial velocity into its horizontal and vertical components. The horizontal component is 42.0 * cos(60°) = 21.0 m/s, and the vertical component is 42.0 * sin(60°) = 36.4 m/s.
In the x-direction, the stone travels at a constant velocity, so the distance x can be found by multiplying the horizontal component of velocity by time: x = 21.0 * 5.50 = 115.5 m.
In the y-direction, the stone is under the influence of gravity. We can use the equation y = y0 + v0y * t - 0.5 * g * t^2, where y0 is the initial height (0 m), v0y is the vertical component of velocity (36.4 m/s), t is the time (5.50 s), and g is the acceleration due to gravity (9.8 m/s^2). Substituting the values, we get y = 0 + (36.4 * 5.50) - (0.5 * 9.8 * 5.50^2) = 198.10 - 150.57 = 47.53 m. Therefore, the stone hits the cliff at a point y of 47.53 m.
The speed of the stone at impact can be found using the equation v = √(v0x^2 + v0y^2), where v0x is the horizontal component of velocity (21.0 m/s) and v0y is the vertical component of velocity (36.4 m/s). Substituting the values, we get v = √(21.0^2 + 36.4^2) = √(441 + 1328.96) = √(1769.96) = 41.97 ≈ 42.0 m/s.
To plot the trajectory of the stone, we can use the equations x = v0x * t and y = y0 + v0y * t - 0.5 * g * t^2. By substituting different values of t, we can calculate the corresponding values of x and y to plot the trajectory.
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