Initial Velocity and Projectiles

[fyzikschik]

Homework Statement

I have a general question. If you were to determine the intial velocity of an object shot vertically into the air, how could you use kinematics equations to predict the height and distance the object would reach if you were then later given a launch angle? Does this mean that the initial velocity is just multiplied by components? I'm really confused. Projectile motion is clearly involved in the second part.. I could measure the time and height when I'm finding the initial velocity, but then what am I using to find height and range at a given angle? Please help without subtlety! Pleease!

Homework Equations

The Attempt at a Solution

 

[OlderDan]

If an object is launched vertically, its maximum height is determined by the launch speed (neglecting any air resistance). Given a height you can calculate the launch speed from

v² = 2gh

If the object is launhed with the same spped, but at an angle θ relative to the horizontal then yes, you need to find the components. The vertical component would be v*sinθ and the height would be found by solving

v²sin²θ = 2gh'

If you divide these two equations you get

h'/h = sin²θ

which is valid only if you are comparing projectiles launced at the same speed but with one vertical and the other at angle θ.

 

[fyzikschik]

Would changing the launch angle change the vertical height?

 

[cristo]

Would changing the launch angle change the vertical height?

See the above equation: v²sin²θ = 2gh', which gives h'= v²sin²θ/2g

Given that v is the same in all cases, and g is the gravitationla field strength constant, can you now answer your question?