Prove that: kinematics/ projectile problem

[jlk]

Homework Statement

A kindly zookeeper, concerned about the health of her prize koala, aims a dart gun at the koala who is sitting in the tree munching on eucalyptus leaves. The koala, feeling a bit under the weather and sensing impending doom, perks up and watches the zookeeper aiming her gun. The wily koala drops from her perch when she sees the dart gun fire and falls to the ground. Does the koala get to the ground to run and hide, or does the dart hit the koala and put it to sleep for a checkup? Prove it with equations and words below. Assume the following: the koala has mass m, the zookeeper (mass M) has perfect aim and is aiming right at the stationary koala (angle theta from the horizontal) in the tree from a distance D away, the koala drops at the same clock reading (or instant) the dart leaves the gun, the koala is height h above the end of the dart gun in the tree, the dart leaves the muzzle of the gun with speed vi which is more than sufficient to reach the koala in the tree. Air friction is negligible.

Homework Equations

The Attempt at a Solution

I don't think mass has any affect on this problem.
However I'm not sure how to start it. is seems like a special relativity problem as well.
hints or helps would be helpful?

 

[alphysicist]

Hi jlk,

Homework Statement

A kindly zookeeper, concerned about the health of her prize koala, aims a dart gun at the koala who is sitting in the tree munching on eucalyptus leaves. The koala, feeling a bit under the weather and sensing impending doom, perks up and watches the zookeeper aiming her gun. The wily koala drops from her perch when she sees the dart gun fire and falls to the ground. Does the koala get to the ground to run and hide, or does the dart hit the koala and put it to sleep for a checkup? Prove it with equations and words below. Assume the following: the koala has mass m, the zookeeper (mass M) has perfect aim and is aiming right at the stationary koala (angle theta from the horizontal) in the tree from a distance D away, the koala drops at the same clock reading (or instant) the dart leaves the gun, the koala is height h above the end of the dart gun in the tree, the dart leaves the muzzle of the gun with speed vi which is more than sufficient to reach the koala in the tree. Air friction is negligible.

Homework Equations

The Attempt at a Solution

I don't think mass has any affect on this problem.
However I'm not sure how to start it. is seems like a special relativity problem as well.

No, the theory of special relativity is not needed here.

Instead think of this as a combination: projectile motion (for the dart) + a 1-D falling motion problem (for the bear). Set them both up separately, and then see if the dart strikes the bear (which means the dart and the bear are at the same position at the same time). How would you find the initial angle of the dart?

 

[jlk]

thanks i got it.

find delta t using the known values of the dart's x direction.

then set the yf of the koala = yf of dart

if the dart hits the koala, they will hit at the same position
that means yf is the same for both

and yes it hits the koala

:)