Motion in 2D snowball problem

[heartofaragorn]

Homework Statement

A snowball picks up speed and rolls of a barn roof angled at 40 degrees from horizontal. The edge of the barn is 15.0 m above the ground, and the snowball has a speed of 7.00 m/s as it leaves the roof. Ignore air effects. How far from the edge of the barn does the snowball land? The trail passing near the barn is 5.0 m horizontally from the barn. How tall would a person have to be to be hit by a snowball when on this trail?

Homework Equations

Range = velocity squared / g X sin 2 theta
Not sure about the others...

The Attempt at a Solution

I think I solved the first question by solving for the range, and the answer I received was 4.92 m. Is this right? I was looking at the second question and got confused because I thought that regardless of how tall the person was, the snowball would fall short. I tried looking at some kinematic equations and had too many variables left. Just a little help going in the right direction would be much appreciated!

 

[cristo]

The range equation will only work if the projectile is shot from the ground and lands back on the ground. You need to use the http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/1DKin/U1L6a.html . Are you familiar with these?

 

[Kurdt]

One knows that the snowball is traveling 7 m/s when it leaves the roof at 40 degrees from the horizontal. You can take the components to find its downward speed and its horizontal speed. then knowing the the acceleration due to gravity is 9.81 m/s² you can solve for the time taken before the snowball hits the ground using kinematic equations (this one isn't easy). Then the distance traveled horizontally will be the horizontal speed multiplied by the time.

 

[heartofaragorn]

I knew exactly what kinematic equation you were speaking of, thank you for the help. I figured the first part out and received an answer of 12.2 m. However, I am still befuddled as to the second question--if someone is on a path that is 5 m from the barn, how tall must they be to be hit with the snowball? I don't understand how someone that's only 5 m away could be hit with an object that lands an extra 7.2 m away from them...do I need to do something with the y-component velocity?

 

[Kurdt]

How far down will the snowball have traveled when its traveled five meters horizontally?

 

[Astronuc]

I don't understand how someone that's only 5 m away could be hit with an object that lands an extra 7.2 m away from them...do I need to do something with the y-component velocity?

The problem is really asking "at what elevation (height) does the snowball pass over the trail, which is 5 m from the barn?"

Another good reference on trajectories is

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html


With vertical acceleration (due to gravity) and horizontal/vertical velocities, the equations of motion define a parabolic trajectory (if negligible air resistance).
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra6

For the given initial conditions, one can determine the vertical position y, as a function of horizontal position, x, or conversely x as function of y.