Question

Deduce the vertical and horizontal components with respect to the initial velocity (u) and angle.

a) u cos θ, u sin θ
b) u sin θ, u cos θ
c) u tan θ, u cot θ
d) u cot θ, u tan θ

Answer 1

The correct deduction for the vertical and horizontal components of initial velocity in projectile motion with respect to angle θ are u sin θ for the vertical component, and u cos θ for the horizontal component.

Step-by-step explanation:

To deduce the vertical and horizontal components with respect to the initial velocity (u) and angle (θ), we look into vector decomposition in projectile motion. In the context of projectile motion, an object's initial velocity (u) can be resolved into two perpendicular components: the horizontal component and the vertical component. The horizontal component of the velocity is given by u cos θ and the vertical component by u sin θ.

For instance, if an object is projected with an initial velocity of 30 m/s at an angle of 45° to the horizontal, its horizontal component of velocity (Ux) is calculated by (30 m/s) cos 45° which equals 21.2 m/s. This is because, in the horizontal direction, there is no acceleration (ax=0), hence the horizontal velocity remains constant throughout the projectile's motion.

Therefore, the correct deduction for the components is: a) u cos θ, u sin θ, corresponding to the horizontal and vertical components, respectively.