Do you like a challenge?

We are going to set up a slanted ramp leading to a level ramp ending at the edge of a table. When we release the ball at the top of the first ramp, it will accelerate as it comes down into the second ramp which will launch it out in an arc from the edge of the table until it hits the floor.

Where will the ball land on the floor? That’s the challenge. Can you calculate where the ball will land?

**Question:** Where will the ball land?

**Materials:**

Two ramps [one must be over a meter long]

Meter stick

Stopwatch

Pan 10 to 15 cm across

Ball

**Procedure:**

Mark out 1 m on the long ramp

Set up the long ramp level on the table top so it ends at the edge of the table

Set up the second ramp on a slant so the bottom end leads into the long ramp

Make sure both ramps are secured in place

Put a barrier at the edge end of the long ramp to stop the ball [a cloth will work]

Mark a starting line near the top of the slanted ramp

Release the ball at the starting mark

Time how fast the ball goes over the marked meter in the long ramp

Repeat this at least three times or until each time is close to the others

Take the barrier out of the long ramp

Measure the distance from the edge of the long ramp to the floor in meters

Calculate the distance the ball will go before hitting the floor [See analysis]

Place your pan with a cloth or sand in it to keep the ball from bouncing where you think the ball will land [Make sure it is straight out from the ramp.]

Note: Be sure you measure from straight down from the edge of the ramp. Why?

Release your ball at the starting mark

If your ball does not land in your pan, try the challenge again

**Observations:**

Velocity times:

Distance to the floor:

**Analysis:**

You have two formulas to work with: d = vt and d = at^{2}.

Remember a is due to gravity and is known to be 9.8 m/s^{2}.

Look back at Physics Project 16 to see which formula tells you how the ball moves, forward or downward. Which values do you know?

Give it a try on your own.

If you have trouble:

When you measure the time it takes for your ball to travel one meter on the long ramp, you have the v for the first equation. The d will be how far the ball goes when it leaves the ramp which you don’t know yet. The time is how long the ball will be in the air when it leaves the second ramp which you also do not know yet.

The height from the edge of the ramp to the floor is the d in the second equation. You also know the a. Use a calculator to solve for t as you must find the square root.

Now you know the t for the first equation and can calculate the d.

Place your bowl.

**Conclusions:**

If your ball missed your bowl, try to figure out why.

**What I Found Out:**

I will admit I do these Projects in a hurry and am often a bit careless in my measurements. That is a recipe for disaster in this challenge.

First problem: The ramps must line up in a straight line or the ball will wobble from side to side or even jump out of the ramp.

Second problem: Both releasing the ball and working the stopwatch. It helps a lot to work with a friend.

Third problem: Measuring the height at which the ball is released accurately if this is not the very top of the ramp. My first measurement was off by almost 2 cm. Also note this measurement is not to the top edge of the ramp but the place the ball is set.

In case you haven’t figured it out by now, my ball missed my bucket for several tries. I redid my height measurement first. This helped. Then I retimed the ball and found I was off by over half a second.

My ball did finally land in the bucket.