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A projectile is given an initial velocity of hat i +2 hat j . The cartesian equation of its path is (g = 10m / (s ^ 2))
(Here i is unit vector along horizontal and is unit vector vertically upwards)?
(Here i is unit vector along horizontal and is unit vector vertically upwards)?
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A projectile is given an initial velocity of hat i +2 hat j . The cart...
Projectile Motion with Initial Velocity
Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration due to gravity. When an object is given an initial velocity, such as in this case where the initial velocity is hat i + 2 hat j, the path of the projectile can be determined using the Cartesian equations of motion.
Cartesian Equation of Path
The Cartesian equation of the path of a projectile can be represented as:
x(t) = v_x * t
y(t) = v_y * t - 0.5 * g * t^2
where:
- x(t) and y(t) are the horizontal and vertical positions of the projectile at time t
- v_x and v_y are the horizontal and vertical components of the initial velocity
- g is the acceleration due to gravity
Determining the Path
Given the initial velocity hat i + 2 hat j, we can break it down into its horizontal and vertical components:
v_x = 1 (horizontal component)
v_y = 2 (vertical component)
Substitute these values into the Cartesian equations of motion:
x(t) = t
y(t) = 2t - 5t^2
Therefore, the Cartesian equation of the path of the projectile is x(t) = t and y(t) = 2t - 5t^2. This equation represents the trajectory of the projectile in terms of time t.
By analyzing the Cartesian equations of the projectile's path, we can understand its motion and predict its trajectory under the influence of gravity.
Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration due to gravity. When an object is given an initial velocity, such as in this case where the initial velocity is hat i + 2 hat j, the path of the projectile can be determined using the Cartesian equations of motion.
Cartesian Equation of Path
The Cartesian equation of the path of a projectile can be represented as:
x(t) = v_x * t
y(t) = v_y * t - 0.5 * g * t^2
where:
- x(t) and y(t) are the horizontal and vertical positions of the projectile at time t
- v_x and v_y are the horizontal and vertical components of the initial velocity
- g is the acceleration due to gravity
Determining the Path
Given the initial velocity hat i + 2 hat j, we can break it down into its horizontal and vertical components:
v_x = 1 (horizontal component)
v_y = 2 (vertical component)
Substitute these values into the Cartesian equations of motion:
x(t) = t
y(t) = 2t - 5t^2
Therefore, the Cartesian equation of the path of the projectile is x(t) = t and y(t) = 2t - 5t^2. This equation represents the trajectory of the projectile in terms of time t.
By analyzing the Cartesian equations of the projectile's path, we can understand its motion and predict its trajectory under the influence of gravity.
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A projectile is given an initial velocity of hat i +2 hat j . The cartesian equation of its path is (g = 10m / (s ^ 2))(Here i is unit vector along horizontal and is unit vector vertically upwards)?
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A projectile is given an initial velocity of hat i +2 hat j . The cartesian equation of its path is (g = 10m / (s ^ 2))(Here i is unit vector along horizontal and is unit vector vertically upwards)? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A projectile is given an initial velocity of hat i +2 hat j . The cartesian equation of its path is (g = 10m / (s ^ 2))(Here i is unit vector along horizontal and is unit vector vertically upwards)? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is given an initial velocity of hat i +2 hat j . The cartesian equation of its path is (g = 10m / (s ^ 2))(Here i is unit vector along horizontal and is unit vector vertically upwards)?.
A projectile is given an initial velocity of hat i +2 hat j . The cartesian equation of its path is (g = 10m / (s ^ 2))(Here i is unit vector along horizontal and is unit vector vertically upwards)? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A projectile is given an initial velocity of hat i +2 hat j . The cartesian equation of its path is (g = 10m / (s ^ 2))(Here i is unit vector along horizontal and is unit vector vertically upwards)? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is given an initial velocity of hat i +2 hat j . The cartesian equation of its path is (g = 10m / (s ^ 2))(Here i is unit vector along horizontal and is unit vector vertically upwards)?.
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