Lab 3.2 Out To Launch

Written by Steve Winiecki Illinois H.S. District 113

The water balloon launcher critical to this lab is called a winger. A funnel, some rubber tubing and some straps to hold on to. See below.

Predict the maximum height and range of a projectile shot at an angle.

Procedures

1.First we need to find the initial velocity of the projectile. If the balloon is shot straight up it will loose its positive velocity at a rate of 9.8 m/s2. When it reaches its maximum height, its positive velocity will be zero. The faster it starts the longer it will take to reach zero velocity and maximum height. Therefore, the maximum height is related to the initial velocity. For a freely falling object the acceleration is the same on the way up as on the way down. So we can imagine the balloon starts at zero velocity at the top and accelerates downward until it reaches its initial position when it will have its same initial speed (not velocity). This view of the problem allows to have a value of zero for v1 which simplifies the equation. The relationships are given below.

a. Dd = v1Dt + 1/2 aDt2 if v1 = 0, a = -9.8 m/s2 and Dd = hmax

hmax = 1/2(-9.8 m/s2)Dt2

b. v2 = v1 + aDt2 if v1 = 0 and a = -9.8 m/s2

v2 = -9.8 m/s2Dt2

2.In order to try to get the same initial speed we need to stretch the launcher the same way each trial. Measure the distance between the arms of the students holding the Winger and the distance the Winger is stretched back. Record these in Table 1.

3. The time in the above equations is only for one way, while the balloon is on the way down. It is easier to see when the balloon returns than when it reaches its maximum height. To get the time on the way down, find the time for the round trip and divide this time by two. Launch and time three balloons. Record these times in Table 2. Calculate maximum height and initial velocity and record these in Table 2. Find the average for height and velocity.

4. You will choose an angle for the launch and then calculate the maximum height and range for this angle. For the angle chosen, draw the initial velocity using the average value from Table 2. Find the vertical and horizontal components for this velocity. Do this in Table 3.

5. For the calculation of the maximum range we need the time the balloon stays in the air. This depends on how long it takes for it to reach a vertical velocity of zero before it starts moving downward. The total time in the air is just twice the time it takes the balloon to reach the top, if it is falling freely. The relationships are given below.

a. a = v2 - v1/Dt Dt = v2 - v1/a

Dt = -vv-(vv)/-9.8 m/s2

Dt = -2vv/-9.8 m/s2

Record your calculated time in air in Table 4.

6.Since the horizontal velocity will be constant for the whole flight, we can use this to find the maximum range of the balloon. The relationships are given below.

a. v = Dd/Dt Dd = vDt

Horizontal distance = range

range = vhDt

Record your calculated range in Table 4.

7.Launch three balloons and find the actual time in air and range for each. Make sure to use the distance between the arms and distance of stretch from Table 1. Record these in Table 4 and find the percent difference for each.

Data

Table 1

Distance between arms (m) Distance of stretch (m)

Table 2

Trial Maximum Height (m) Initial Velocity (m/s)

1

2

3

Average

Table 3

Initial velocity vector Vertical Component Horizontal Componet

Table 4

Trial Calculated time (s) Calculated range (m) Actual time

(s) Actual range (m) Percent difference for time Percent difference for range

1

2

3

4

Analysis Questions

1.Our equations are true if the balloon returns to the same height at which it left. This is not true since we launch the balloon about 1.5 m above the ground and it lands on the ground. How will this effect our experimental value to the theoretical value?

2. The initial velocity of the "human cannonball" is 9.0 m/s at an angle of 60o above the horizontal. When the human cannonball reaches a vertical displacement of zero we would like her to land in a net. How far away should the net be placed? Show your work!

Conclusion