A mod 5 q (1 Viewer)

[yashbb]

Can someone explain to me why an increase in the launch angle of a projectile increases the final velocity. Is v not meant to be equal to u?

 

[ExtremelyBoredUser]

Can someone explain to me why an increase in the launch angle of a projectile increases the final velocity. Is v not meant to be equal to u?

Horizontal velocity is only equal to initial horizontal velocity since Horizontal Acceleration is assumed to be 0. This assumption is not exclusive to one question and is like that for Mod 5 Projectile motion.

Vertical velocity on the other hand is NOT equal to initial vertical velocity since Vertical Acceleration is gravity acting on the projectile, so on Earth it would be 9.8 or on Moon it would be 1.67. The question would specify the value for acceleration.

When you increase the launch angle, you are increasing the initial vertical velocity likewise. You can see this intuitively as when you aim something with a greater angle, it goes further up rather than horizontal. Understanding this mathematically, Uy = Usin(A) where A is the angle. When the angle is increased, the sin(A) component increases meaning the vertical initial velocity increases as well as Uy = U * sin(A) and likewise the initial horizontal velocity decreases Ux = Ucos(A) and cos(A) component consequently decreases as the angle increases.

To answer your question now... The final velocity is equivalent to the Initial Horizontal Velocity (as it does not change since we assume horizontal acceleration to be 0) + the final vertical velocity (Initial vertical velocity * time of flight)



You can find vertical velocity through other ways such as the suvat equations v^2 = u^2 + 2gs or v = u + at.

 

[yashbb]

Horizontal velocity is only equal to initial horizontal velocity since Horizontal Acceleration is assumed to be 0. This assumption is not exclusive to one question and is like that for Mod 5 Projectile motion.

Vertical velocity on the other hand is NOT equal to initial vertical velocity since Vertical Acceleration is gravity acting on the projectile, so on Earth it would be 9.8 or on Moon it would be 1.67. The question would specify the value for acceleration.

When you increase the launch angle, you are increasing the initial vertical velocity likewise. You can see this intuitively as when you aim something with a greater angle, it goes further up rather than horizontal. Understanding this mathematically, Uy = Usin(A) where A is the angle. When the angle is increased, the sin(A) component increases meaning the vertical initial velocity increases as well as Uy = U * sin(A) and likewise the initial horizontal velocity decreases Ux = Ucos(A) and cos(A) component consequently decreases as the angle increases.

To answer your question now... The final velocity is equivalent to the Initial Horizontal Velocity (as it does not change since we assume horizontal acceleration to be 0) + the final vertical velocity (Initial vertical velocity * time of flight)



You can find vertical velocity through other ways such as the suvat equations v^2 = u^2 + 2gs or v = u + at.

Ahh i see, thank you so much man!