How Fast Must a Baseball Travel to Clear a 29m Obstacle?

[MissJewels]

Homework Statement

A baseball is hit at a height of 1m with an initial speed of vo module at an angle of projection of 35o from the horizontal. She spent just over an obstacle of 29m high at a horizontal distance of 64m.
Find
a) vo
b) the time it takes to reach the OBSTACLES
c) its speed at the obstacle.

Homework Equations

Xi= 0
Xf= 64
Yi= 1
Yf= 29

Equations: Yf= Vosin(35) -9,8t

The Attempt at a Solution

Not too sure how to go about with this one. I end up with two variables in the equations i use. help!

 

[Andrew Mason]

Homework Statement

A baseball is hit at a height of 1m with an initial speed of vo module at an angle of projection of 35o from the horizontal. She spent just over an obstacle of 29m high at a horizontal distance of 64m.
Find
a) vo
b) the time it takes to reach the OBSTACLES
c) its speed at the obstacle.

Start with:

v_x = v_0\cos(\theta)

v_y = v_0\sin(\theta) - gt

What are the equations for the height and range as a function of time?

Set height at 29 m and at horizontal range 64 m. Plug the values for x, y into these equations. From that you should be able to determine v_0.

AM

 

[MissJewels]

Start with:

v_x = v_0\cos(\theta)

v_y = v_0\sin(\theta) - gt

What are the equations for the height and range as a function of time?

Set height at 29 m and at horizontal range 64 m. Plug the values for x, y into these equations. From that you should be able to determine v_0.

AM

Sorry it took a while, here's what I did... something's off...
just part a)

 

[Andrew Mason]

From the first equation:

t = 64/v_0\cos{(35)}

Substitute that value for t into the second equation:

y = y_0 + v_{0}\sin{(35)}t - \frac{1}{2}gt^2

It gets a little hairy with a quadratic equation but I think it is a little easier to solve for v0 than for t.

AM