Problem Theory

AP Physics B

Name_________________________

An experiment to determine the maximum height and horizontal range of a projectile launched at a given angle above the horizontal.

Problem: Can we hit a target by using theoretical calculations of maximum height and horizontal range?

Theory: When a projectile leaves a launcher it experiences downward acceleration due gravity. The path

of projectile is a parabola. We can apply the equation of acceleration motion to find the maximum

height and horizontal range:

X= Xo + Voxt + ? axt2 or Y= Yo + Voyt + ? ayt2 or

X = Vo cos t (1) Y= Vosin t ? ? at2 (2)

When we substitute zero instead of y-component, we can calculate the time of flight:

t=2Vosin/g

We can substitute the time of flight in (1), and calculate the horizontal range of the projectile:

R=Vo2sin2/g

(3)

To determine the maximum height of flight, we substitute a half of time of flight in (2):

Hmax= Vo2sin2/2g

(4)

During this investigation you make the theoretical calculations of the maximum height and horizontal

range of a projectile. Then you place one ring (target) at a distance R from the launcher, another ring

(target) at the Hmax, and when you launch the ball you have to hit the targets.

Vy=0 at this point

o

a=g

Materials: launcher, ball, ruler, stands, and rings. Procedure:

1. Arrange the launcher vertically, and project a ball 3-5 times (use first notch). For each trial, measure the maximum height.

2. Find the average height, and using the formula Vo = 2avg 3. Substitute Vo and =45o in (3), and calculate the horizontal range R (at 45o). Record the number

in Table 1. 4. Substitute Vo and =45o in (4), and calculate the maximum height Hmax (at 45o). Record the

number in Table 1.

5. Place the lab stand with a ring at the distance R from the launcher (at the same vertical level as the launcher is).

6. Place the lab stand with a ring at R/2 from the launcher at Hmax (the vertical level of the launcher is zero).

7. Arrange the launcher at 45o, and project the ball. If you made the right calculations, you will hit the targets.

8. Repeat steps (3-7) for 30o and 60o.

Trial

Angle

Initial velocity, Horizontal Range, Maximum

(m/s)

(m)

Height, (m)

1

2

3

Conclusion: Make the conclusion about you major result.

Questions: 1. Which factors can affect the results?

2. Can we apply the major result in daily life? Explain.

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