How Far Should Goods Be Dropped from a Plane to Hit a Mountain Ridge?

[schrock]

I am trying to drop goods to a ridge of a mountain. The height from the ground to the plane is 203 m. The distance from the plane to the ridge is X. If plane is traveling at 65.278 m/s, how far in advance (horizontal distance) must the goods be dropped?

-Should I calculate Vxo since Vyo would be 0? Then figure out what the horizontal distance would be?

Using same info, what if now 441 m in advance of drop zone, what vertical velocity should supplies be given to hit drop zone?

 

[mgb_phys]

The technique is generally to calculate the time the object will take to fall the appropriate distance (assuming no air resistance and falling at 'g')
You then use this time together with the constant horizontal speed to calculate the horizontal distance

 

[baba89]

I would suggest using the equations of motion to calculate the necessary information for this scenario. The horizontal distance (X) can be calculated using the formula X = Vx * t, where Vx is the horizontal velocity of the plane and t is the time it takes for the goods to reach the ridge. In this case, the time can be calculated by dividing the height (203m) by the vertical velocity (Vy) of the goods, which can be found using the equation Vy = Vyo + gt, where Vyo is the initial vertical velocity (which is 0 in this case) and g is the acceleration due to gravity (9.8 m/s^2). Once Vy is calculated, it can be used to find the time (t) and then plugged into the equation for X to determine the necessary distance in advance for the goods to be dropped.

For the second question, if the goods are now being dropped 441m in advance, the vertical velocity of the goods would need to be greater to reach the drop zone. This can be calculated using the equation Vyo = (X/t) - (1/2)gt^2, where X is the horizontal distance (441m) and t is the time it takes for the goods to reach the drop zone. Again, t can be calculated using the equation t = X/Vx. Once Vyo is determined, it can be used to calculate the necessary vertical velocity for the goods to reach the drop zone.

Overall, it is important to consider the equations of motion and the given variables in order to accurately determine the distance and velocity needed for the goods to be dropped successfully.