Question that I answering [projectile motion]

[bee24]

Okay, can someone help me figure out this problem. I've tried a lot of things but then i just get lost in all my sine and cosine mess that ends up confusing me.

[values changed for simplicity reasons]

-The pitcher is going to throw a ball from 4 meters above the ground and there is a distance of 20 m to the batter. A pitcher stands on the mound and throws the ball at an angle of @[theta] with respect to the horizon with the initial speed of 40 m/s. At what angle should the ball be thrown so that the ball will land 2 meters above the ground when it reaches the batter?

so the data is as follows:

initial starting point of ball: 4 meters above ground (y) and 20 meters from the batter (x)
final point of the ball: 2 meters above the ground (y)and 20 meters from the original point (x)
initial speed is 40 m/s at the unknown angle of @[theta]

so basically, i guess what I'm asking here is how to split the initial velocity into x and y components.

thank you if you can help me,
and thanks for trying if u can't. O.O

 

[Hootenanny]

You are correct that you need to take components of the initial velocity then use kinetmatic equations to solve two simultaneous equations to find \theta. Have you taken components before? Seen any worked examples in class? It does involve a small amount of trig.

 

[bee24]

I have, but not a lot of experience outside of mechanical solving using kinematic solving that actually requires generalizations. Any help is appreciated.

 

[Hootenanny]

Okay, so you know the intial speed is 40 m.s^-1. This speed is has a direction of \theta degrees above the horizontal. Now, can you use trigonometry to determine the horizontal and vertical components of the initial velocity?

 

[bee24]

Okay thanks Hootenanny but I figured it out. Greatly appreciate it though.