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.