A body is projected upwards at any an angle of 30 degree with the horizontal and intial speed of 200 ms^1 in how many seconds Will it teach the group? How far from the point of projection will it strikes?
...teach the group??
the range is ... R = [v^2 * sin(2Θ)] / g
... v is the launch velocity ... 200 m/s
... Θ is the launch angle ... 30º
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To find the time it will take for the body to reach the ground, we can break down the initial velocity into its vertical and horizontal components.
The vertical component of the initial velocity can be calculated as:
V_initial_vertical = V_initial * sin(theta)
where:
V_initial = initial speed = 200 m/s
theta = angle of projection = 30 degrees
V_initial_vertical = 200 m/s * sin(30 degrees)
V_initial_vertical = 100 m/s
Now, knowing that the acceleration due to gravity is approximately 9.8 m/s² and the initial vertical velocity is 100 m/s, we can use the kinematic equation:
V_final = V_initial + (a * t)
where:
V_final = final velocity = 0 m/s (as the body will reach its maximum height)
V_initial = initial velocity = 100 m/s
a = acceleration due to gravity = -9.8 m/s² (negative because it opposes the motion)
t = time it takes to reach maximum height (also the time it takes to fall back down)
Substituting the values into the equation:
0 = 100 - 9.8 * t
Simplifying the equation:
9.8 * t = 100
t = 100 / 9.8
t ≈ 10.20 seconds (rounded to two decimal places)
Therefore, it will take approximately 10.20 seconds for the body to reach the ground.
To find the horizontal distance the body will travel, we can use the horizontal component of the initial velocity and the time it takes to reach the ground.
The horizontal component of the initial velocity can be calculated as:
V_initial_horizontal = V_initial * cos(theta)
where:
V_initial = initial speed = 200 m/s
theta = angle of projection = 30 degrees
V_initial_horizontal = 200 m/s * cos(30 degrees)
V_initial_horizontal = 173.21 m/s (rounded to two decimal places)
To find the distance traveled, we can use the equation:
Distance = V_initial_horizontal * t
where:
V_initial_horizontal = horizontal component of initial velocity = 173.21 m/s (rounded)
t = time it takes to reach the ground = 10.20 seconds (rounded)
Distance = 173.21 m/s * 10.20 seconds
Distance ≈ 1767.57 meters (rounded to two decimal places)
Therefore, the body will strike the ground approximately 1767.57 meters away from the point of projection.