Why in projectile motion u sin theta is varying but u cos theta is constant?

Question

Answer

Because in vertical direction there is acceleration due to gravity while in horizontal there is no any acceleration

Answer

Explanation of why u sin theta is varying but u cos theta is constant in projectile motion

Definition of projectile motion: Projectile motion is the motion of an object that is projected into the air and then moves under the influence of gravity.

Horizontal and vertical components of velocity: The motion of a projectile can be broken down into two components: the horizontal component and the vertical component. The horizontal component of the velocity remains constant throughout the motion, while the vertical component changes due to the effect of gravity.

Initial velocity: At the beginning of the motion, the object is given an initial velocity (u) at an angle (theta) with respect to the horizontal plane. This initial velocity can be broken down into its horizontal and vertical components, which are u cos theta and u sin theta, respectively.

Horizontal component of velocity: The horizontal component of velocity (u cos theta) remains constant throughout the motion because there is no force acting on the projectile in the horizontal direction. Therefore, the projectile continues to move at a constant speed in the horizontal direction.

Vertical component of velocity: The vertical component of velocity (u sin theta) changes throughout the motion due to the effect of gravity. As the projectile moves upward, the vertical component of velocity decreases until it reaches its maximum height, where it becomes zero. Then, as the projectile moves downward, the vertical component of velocity increases until it reaches its maximum value just before hitting the ground.

Conclusion

In conclusion, u sin theta is varying but u cos theta is constant in projectile motion because the horizontal component of velocity remains constant throughout the motion while the vertical component changes due to the effect of gravity. Therefore, the initial velocity can be broken down into its horizontal and vertical components, which are u cos theta and u sin theta, respectively. The horizontal component of velocity remains constant because there is no force acting on the projectile in the horizontal direction, while the vertical component changes due to the effect of gravity.

Answer

U sin theta varies because the acceleration in y direction is present i.e. gravitational acceleration down the earth....however it isn't so in u cos theta direction which is x direction.!!!

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