Projectile Motion Problem with 2 Moving Cars

[calwonderman]

Goodmorning, here is the problem that has troubled me and a bunch of my friends much of the day.

A low-flying helicopter is flying a constant 200 km/h horizontally wants to drop a object into a open car which is traveling at 150 km/h on a level highway 78.0 m below. At what angle (with the horizontal) should the car be in his sights when the packet is released?

This problems is troubling me somewhat because I do not understand if it is free falling or there is some initial velocity conversion that I have been overlooking. Unforuntaley the pythagorean theorem has escaped my rational as does the idea that speed cannot be attained without some type of initial speed given. I am completely lost, I know some concept has to with the relative speeds each car has, yet it troubles me.

Please help in anyway shape or form. Thank you!

 

[SGT]

You know the time the object will take to drop 78 m under the acceleration of gravity.
You know also the difference between the horizontal speeds of the helicopter (and object) and the car. How far will the object travel relative to the car?
You have two sides of a right triangle (height and horizontal distance), so you can obtain the sight angle.

 

[wais]

Hi there,

Thank you for reaching out for help with this projectile motion problem. I can understand why it may be causing confusion for you and your friends. Let's break it down and try to understand the key concepts involved.

First, let's consider the motion of the object being dropped from the helicopter. As it is released, it will have an initial horizontal velocity of 200 km/h (assuming no air resistance). However, it will also have a vertical velocity due to the force of gravity acting on it. This means that the object will follow a parabolic path as it falls towards the ground.

Next, let's consider the motion of the car. It is traveling at a constant speed of 150 km/h horizontally, but it is also moving vertically due to the curvature of the Earth. This vertical motion can be ignored for this problem, as it is negligible compared to the height of the helicopter.

Now, in order for the object to land in the car, it must have the same horizontal velocity as the car at the moment of impact. This means that the object must be dropped at an angle that allows it to have a horizontal velocity component of 150 km/h.

To find this angle, we can use the formula for horizontal velocity:

Vx = V * cos(theta)

Where Vx is the horizontal velocity, V is the initial velocity (in this case, 200 km/h), and theta is the angle between the velocity and the horizontal. We know that Vx must be equal to 150 km/h, so we can solve for theta:

150 km/h = 200 km/h * cos(theta)

cos(theta) = 150/200

theta = cos^-1(150/200) = 48.6 degrees

Therefore, the car should be at an angle of 48.6 degrees with the horizontal when the object is dropped from the helicopter.

I hope this helps clarify the problem for you. Keep in mind that this solution assumes ideal conditions and does not account for factors such as air resistance or the curvature of the Earth. Let me know if you have any other questions or need further clarification. Good luck!