Problem: Given Angle and Distance

[dakinecuz]

Homework Statement

A baseball leaves the bat at 31 degrees of the horizontal. The ball was caught by an outfielder 400 ft from the home plate. The height where the ball was hit is the same where it was caught by the outfielder.

whats the initial speed of the ball?
whats the maximum height it reaches?

Homework Equations

1. y = y0 + voyt + (1/2)(g)(t)^2
2. vy = v0y + (g)t

The Attempt at a Solution

This is where it got a little messy.
First off:
I converted 400 ft to meters getting 121.9 m.
After that, from the pythagorean theorem: See pic 1.

After, i figured that at the half distance of 121.9m (60.95m) the Vy = 0.
I then used the theorem of ratio of triangles to find the maximum height would be if gravity is 0. The max height would be 36.6 m. see pic 2.

Since i don't have the time, i got t from equation 2 and substituted it in equation 1. I eventually derived (v0y)^2 (30/196) = y

Substitute y for 36.6m
i got v0y = 15.46m

and from there I just derived everything else from that number.

v0 = 30 m/s
max height = 12.17 m

help is appreciated. Thanks in advance.
Chris

 

[learningphysics]

The ball does not follow a straight line path along 31 degrees... so you can't use the pythogrean theorem to get the maximum height.

What is the equation for horizontal displacement in terms of time, v0, theta...

What is the equation for vertical displacement in terms of time, v0, theta...

 

[m2003]

Hello Chris,

Thank you for sharing your solution attempt with me. Your approach seems to be on the right track, but there are a few things that I would like to clarify and suggest in order to improve your solution.

Firstly, when converting 400 ft to meters, you should get 121.92 m, not 121.9 m. It's important to be precise with your calculations to avoid any errors in your final result.

Secondly, I'm not sure what you mean by "if gravity is 0". Gravity is a constant force on Earth and cannot be turned off. However, it's possible that you meant to say "if air resistance is neglected". In that case, you can use the maximum height formula h = (v0^2 sin^2θ)/(2g) to find the maximum height without considering air resistance.

Additionally, it's not clear how you derived the equation (v0y)^2 (30/196) = y. It would be helpful if you could explain your reasoning behind this step.

Overall, your final answer of v0 = 30 m/s and max height = 12.17 m seems reasonable. However, it would be beneficial to show your calculations and steps in a more organized and clear manner. This will help you and others to better understand your solution and ensure that there are no mistakes.

I hope this helps and good luck with your future problem-solving!