Will a Projectile Hit a Falling Target If Fired Simultaneously?

[LastBloomingFlower]

I started out drawing pictures and I can't get any farther...

50. In a very popular lecture demonstration, a projectile is fired @ a falling target. The projectile leaves the gun the same instant that the target is dropped from rest. Assuming that the gun is initially aimed at the target, show that the projectile will hit the target.

51. An enemy ship is on the east dide of a mountainous island. The enemy ship can maneuver to within 2500 m of a the 1800-m high mountain peak and can shoot projectiles with an initial speed of 250 m/s. If the western shoreline is horizontally 300 m from the peak, what are the distances from the western shore at which a ship can be arfe from the bombardment of the enemy ship?

 

[Dorothy Weglend]

I'm sure you know that the x and y components of the motion of a projectile are independent of each other. Try applying this idea to both of these problems.

Dorothy

 

[turdferguson]

For 50, both the projectile and the target are accelerating at g. When the projectile catches up to the target, they will have fallen the same vertical distance

 

[LastBloomingFlower]

Any help for 51?

 

[turdferguson]

With trig, find the minimum angle the ship can shoot from. Then use the range formula to find the possible distances

 

[andrevdh]

50. Try this: Set the positional equations up for both objects in the same coordinate system. Choose the y-axis going through the object that drops straight down. Then show that when the x-coordinate of the object with the projectile motion is zero the y-coordinates of both are the same.

51. The peak is at an elevation of $$35.8^o$$ with respect to the enemy ship. This means that the safe distance will be just beyond the maximum range of the enemy ship, which is obtained when the enemy ship fire at an angle of $$45^o$$.