Experiment: Function and Mini Launcher
Experiment 3: Projectile Range Versus Angle
EQUIPMENT NEEDED
– Mini Launcher and steel ball
– Plumb bob
– Measuring tape or meter stick
–
Carbon paper
– Graph paper
–
White paper
Purpose
The purpose of this experiment is to find how the range of the ball depends on the angle at which it is launched. The angle that gives the greatest range is determined for two cases: launching on level ground and launching off a table.
Theory
The range is the horizontal distance, x, between the muzzle of the Launcher and the place where the ball lands. The range is given by x = (v0cosθ)t, where v0 is the initial speed of the ball as it leaves the muzzle, θ is the angle of inclination above horizon-tal, and t is the time of flight. See figure 3.1.
v0
θ
x
Figure 3.1: Shooting on a level surface
For the case in which the ball lands at the same elevation from which it was launched, the time of flight of the ball will be twice the time it takes the ball the reach the peak of its trajectory. At the peak, the vertical velocity is zero so
vy = 0 = v0 sinq - gt peak
Therefore, solving for the time gives the total time of flight as t = 2t peak = 2 v0 sinθ
.
g
For the case in which the ball is launched at an angle from a table onto the floor, (See Figure 3.2) the time of flight is found using the equation for the vertical motion:
y = y0 + v0 sinq t - 12 gt2
v0
θ
y0
x
Figure 3.2: Shooting off the table
® 15
Mini Launcher
012-05479B
where yo is the initial height of the ball and y is the position of the ball when it hits the floor.
Setup
➀ Clamp the Mini Launcher near one end of a sturdy table with the Launcher aimed so the ball will land on the table. The square nut in the T-slot should be positioned near the muzzle.
➁ Adjust the angle of the Mini Launcher to ten degrees.
➂ Put the steel ball into the Mini Launcher and cock it to the chosen position.
Procedure
EQUIPMENT NEEDED
– Mini Launcher and steel ball
– Plumb bob
– Measuring tape or meter stick
–
Carbon paper
– Graph paper
–
White paper
Purpose
The purpose of this experiment is to find how the range of the ball depends on the angle at which it is launched. The angle that gives the greatest range is determined for two cases: launching on level ground and launching off a table.
Theory
The range is the horizontal distance, x, between the muzzle of the Launcher and the place where the ball lands. The range is given by x = (v0cosθ)t, where v0 is the initial speed of the ball as it leaves the muzzle, θ is the angle of inclination above horizon-tal, and t is the time of flight. See figure 3.1.
v0
θ
x
Figure 3.1: Shooting on a level surface
For the case in which the ball lands at the same elevation from which it was launched, the time of flight of the ball will be twice the time it takes the ball the reach the peak of its trajectory. At the peak, the vertical velocity is zero so
vy = 0 = v0 sinq - gt peak
Therefore, solving for the time gives the total time of flight as t = 2t peak = 2 v0 sinθ
.
g
For the case in which the ball is launched at an angle from a table onto the floor, (See Figure 3.2) the time of flight is found using the equation for the vertical motion:
y = y0 + v0 sinq t - 12 gt2
v0
θ
y0
x
Figure 3.2: Shooting off the table
® 15
Mini Launcher
012-05479B
where yo is the initial height of the ball and y is the position of the ball when it hits the floor.
Setup
➀ Clamp the Mini Launcher near one end of a sturdy table with the Launcher aimed so the ball will land on the table. The square nut in the T-slot should be positioned near the muzzle.
➁ Adjust the angle of the Mini Launcher to ten degrees.
➂ Put the steel ball into the Mini Launcher and cock it to the chosen position.
Procedure