[Math] Calculus III Vectors – Projectile problem

calculusvectors

A projectile is fired from ground level with an initial speed of $450 m/sec$ and an angle of elevation of 30 degrees. Use that the acceleration due to gravity is $9.8 m/sec^2$.
The range of the projectile is ____ meters.
The maximum height of the projectile is ____ meters.
The speed with which the projectile hits the ground is ____ m/sec.

I have deduced the range to be $17894.91268 m$ by using the example from the lecture. However, the discussion on how to solve the rest of this problem only left me more confused. Any help would be greatly appreciated. Thank you!

Best Answer

The greatest height is given by $H=\frac{V^2\sin^2\alpha}{2g}$ and the particle will hit the ground with the same speed as the speed of projection, due to conservation of energy. All of this is assuming that air resistance is negligible.

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