Chuckin' Rocks at Walls

Suppose I walk toward a wall at 1.5 m/s, taking 1.5 steps per second, and on every second step I chuck a rock at the wall.

• If the rock speed, relative to the ground, is 10 m/s then how long will it be between collisions of the rocks with the wall?
• How will the number of collisions per minute compare with the number of rocks thrown per minute?

Suppose I now walk away from the wall at the same speed and again chuck rocks at the wall, one rock every two steps, and I flang the rocks a little faster so they'll still be moving at 10 m/s relative to the ground.

• Now how will the number of collisions with the wall per minute compare with the number of rocks thrown per minute?

Chuckin' Rocks into the Pond

Now I want to throw rocks into the pond. I throw a rock and observe that when it strikes the water it causes waves to spread out in a circular pattern, moving at about .6 meter/sec. I notice also that waves of different sizes travel at different speeds, but for now I concentrate on the fastest wave, the one at the outer rim of the circle.

If I throw four rocks into the pond so that they hit .9 meters apart, one after another along a straight line and times so that they hit the water 1/2 second apart, what will the wave pattern look like at the instant the last rock hits?

• What will the pattern look like 1/2 second after the last rock hits, then 1/2 second after that, then 1/2 second after that?
• Sketch a picture to depict what happens as the waves spread out.

What would the pattern look like if the rocks hit only 1/4 second apart? How would it differ from the preceding picture?

What would each of the above patterns look like if there were a lot of rocks hitting along the same line, from the starting point to the point 2.7 meters away where the last rock hit in the previous example, with the entire process still taking place in the 1.5 seconds between the first and last rock?

More Pond Rock Chuckin'

Suppose I stand on a platform above the middle of the pond and drop a rock into the water, one rock every 2 seconds, while a friend standing 2 meters away on the other side of the platform also drops rocks at 2-second intervals but staggered with mine so that every second a rock gets dropped by one of us.

• After 10 seconds what does the pattern of waves in the pond look like?
• Where will the wave disturbance be greatest and where will it be least?