A body is projected at angle of 30 degree with the horizontal at an initial speed of 200m/s.how far from the point of projection will it strike
Range = Vo^2*sin(2A)/g=200^2*sin(60)/9.8 = 3535 m.
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3535 metres
Henry
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To find the distance from the point of projection where the body will strike, you can use the equations of motion for projectile motion.
First, let's break down the initial velocity into its horizontal and vertical components. The horizontal component of the initial velocity is calculated by multiplying the initial speed by the cosine of the launch angle:
Horizontal component = initial speed * cos(angle)
Substituting the given values, we get:
Horizontal component = 200 m/s * cos(30°)
Next, let's calculate the time of flight. The time of flight is the total time the object is in the air before it lands, and it is given by the equation:
Time of flight = (2 * vertical component of initial velocity) / (acceleration due to gravity)
The vertical component of the initial velocity can be calculated by multiplying the initial speed by the sine of the launch angle:
Vertical component = initial speed * sin(angle)
Substituting the given values, we get:
Vertical component = 200 m/s * sin(30°)
Now, the acceleration due to gravity is approximately 9.8 m/s².
Time of flight = (2 * vertical component) / (acceleration due to gravity)
Finally, we can use the equation for distance traveled horizontally during projectile motion:
Distance = horizontal component * time of flight
Substituting the calculated values, we get:
Distance = (200 m/s * cos(30°)) * ((2 * 200 m/s * sin(30°)) / 9.8 m/s²)
Simplifying the equation, we find:
Distance = (200 * √3 / 2) * ((2 * 200 * 1 / 2) / 9.8)
Now, calculating this further:
Distance = (√3 * 200) * (400 / 9.8)
Distance ≈ 11586.74 meters (rounded to two decimal places)
Therefore, the object will strike the ground approximately 11,586.74 meters away from the point of projection.