A stone is projected as an angle of 60% and initial velocity of 20ms/1 determine
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To determine the trajectory of a stone that is projected at an angle of 60 degrees with an initial velocity of 20 m/s, you can follow these steps:
Step 1: Resolve the initial velocity into its horizontal and vertical components.
The initial velocity of 20 m/s can be broken down into its horizontal and vertical components using trigonometry. The horizontal component (Vx) can be determined using the equation Vx = V * cos(θ), where V is the initial velocity and θ is the launch angle. The vertical component (Vy) can be determined using the equation Vy = V * sin(θ).
In this case, the launch angle is 60 degrees, so Vx = 20 m/s * cos(60°) and Vy = 20 m/s * sin(60°).
Step 2: Analyze the motion of the stone in the horizontal direction.
Since there are no horizontal forces acting on the stone, its horizontal velocity remains constant throughout its motion. Therefore, the stone's horizontal velocity (Vx) will remain the same.
Step 3: Analyze the motion of the stone in the vertical direction.
In the vertical direction, the stone is under the influence of gravity, causing it to undergo projectile motion. The vertical velocity (Vy) will change over time due to the acceleration caused by gravity.
The equation that represents the vertical motion of the stone is given by the equation: h = Vyt - (1/2) * g * t^2, where h is the vertical displacement, Vy is the initial vertical velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Step 4: Analyze the time of flight and maximum height reached.
To find the time of flight (the total time the stone is in the air), we need to determine when the stone returns to the same level from where it was launched. At this point, the vertical displacement (h) will be zero.
Setting h = 0 in the equation, we get 0 = Vyt - (1/2) * g * t^2. Solve this equation to find the time of flight (t_flight).
The maximum height (h_max) reached by the stone can be found by finding the maximum value of h during its vertical motion. To do this, we can use the equation Vy = 0 at the highest point of its trajectory.
Step 5: Analyze the horizontal range.
The horizontal range (R) is the horizontal distance covered by the stone before hitting the ground. To find this, we can use the equation: R = Vx * t_flight, where Vx is the horizontal velocity and t_flight is the time of flight determined in Step 4.
By following these steps and plugging in the values given, you can determine the trajectory of the stone projected at an angle of 60 degrees with an initial velocity of 20 m/s.