Finding Initial Velocity of a Projectile Using Position and Angle

[JoeTrumpet]

I've been having trouble with problems of this sort (determining initial velocity or a projectile when a position and initial angle are given). Here's one in particular:

Homework Statement

A baseball is hit so that the baseball just clears the top row of bleachers, 21m high, located 130m from the home plate. The ball is hit at an angle of 35 degrees to the horizontal, and air resistance is negligible. Find the initial speed of the ball. Assume the ball is hit at a height of 1m above the ground.

Homework Equations

The only equation I have involving the initial angle only determines the component vectors, eg, cos(theta) = vxi/vi.

The Attempt at a Solution

I really can't even begin to do anything useful. Any help would be greatly appreciated! (The answer is 41.7m/s, but I have no idea how to reach that.)

 

[Astronuc]

See these examples for trajectory.
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

Look for - "Will it clear the fence?"

Now the significance of being hit at 1 m means to put in on the same plane, simply subtract 1 m from the height of the object it clears, which in this case is 21 m.

 

[rocomath]

Now the significance of being hit at 1 m means to put in on the same plane, simply subtract 1 m from the height of the object it clears, which in this case is 21 m.

ah damn! i added rather than subtracting, I'm still new to physics. pretty strange

now that i think about it, it doesn't make sense to add.

 

[JoeTrumpet]

See these examples for trajectory.
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

Look for - "Will it clear the fence?"

Now the significance of being hit at 1 m means to put in on the same plane, simply subtract 1 m from the height of the object it clears, which in this case is 21 m.

Unfortunately, this doesn't seem to answer my question. That example assumes I know the initial velocity, which is what I'm trying to figure out. I apologize if I misunderstood the solution.

 

[rocomath]

what book is this from? i really want to help you, perhaps if you have Univ. Physics - Young?

 

[JoeTrumpet]

what book is this from? i really want to help you, perhaps if you have Univ. Physics - Young?

This is from Physics for Scientists and Engineers 6th edition by Serway. The solution is said to be in the solutions manual, but I don't have that. :(

 

[hage567]

You need to set up the equations of motion in both directions, the vertical and the horizontal. The link Astronuc gave you can help you with this. Once you have the equations describing the motion, you can put them together to find the initial velocity.

 

[JoeTrumpet]

Wow, when I started writing out this reply I didn't get it, but in the middle of it I did! But just to double check that this is the most elegant method...

I started with.

x = (vxi)t
y = (vyi)t - 4.9t^2

I then derived the following

t = x/(vxi) and substitute it into
y = (vyi)t - 4.9t^2 to get
y = x(vyi)/(vxi) - (x^2)(4.9)/((vxi)^2)

What I did was change vyi/vxi to tan(35) and solve for vxi then substitute vxi into tan(35) = vyi/vxi and solved for vyi. Was the problem meant to have so much substitution or did I overcomplicate something? Either way, thank you, everyone, so much for all your help! It was a great feeling to finally get it.