What is the vertical height between two climbers?

[afcwestwarrior]

Homework Statement

A rock climber throws a small first aid kit to another climber who is higher up the mountain. The initial velocity of the kit is 11 m/s at an angle of 65 degrees above the horizontal. At the instant when the kit is caught, it is traveling horizontally, so it's vertical speed is zero. What is the vertical height between the 2 climbers.

Initial Velocity=11 m/s
Angle above horizontal=65 degrees
Vertical speed=0

Homework Equations

equations of kinematics

The Attempt at a Solution

 

[Astronuc]

Please show some work and effort on one's part.

Initial Velocity=11 m/s

Determine the horizontal and vertical velocity components.

The horizontal velocity is constant if one ignores air resistance. The kit decelerates as it travels vertically.

Refer to -
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra5

 

[afcwestwarrior]

Here is what I did. I used the equation y=h=Vy^2 - Voy^2/ 2 (Ay)

Then I used the values I had h=(0m/s)^2 - (11 m/s)^2/ 2 (-9.8m/s^2) = 6.1 meters

The answer is 5.1 meters what did I do wrong

 

[Astronuc]

v_y0 is not 11 m/s.

v₀ = 11 m/s.

Resolve v₀ into v_y0 and v_x0

Think about sin and cos of the angle with respect to horizontal.

 

[afcwestwarrior]

ok Vy0=11 sin 65=10 m/s
and Vx0=11 cos 65=4.6 m/s

Now what do I do

 

[afcwestwarrior]

Ok so it's h=0 m/s)^2 - 10 m/s) ^2/2 *-9.8 m/s^2=5.1

 

[afcwestwarrior]

Did I do it right

 

[Astronuc]

Yes!

 

[afcwestwarrior]

Thank you Astronuc. It feels good learning how to solve a problem. Instead of just writing down the answer.

 

[mr_schticker]

Thanks!

Thanks so much, I had the same problem. Ironically, I had split it up into components already, just for some reason I hadn't added it into the formula as my VoY, I was still using the old Vo vector.

Thanks!