Use a stopwatch to measure the total time t it takes the ball to land in the bucket.

Angle the launcher at a 45° angle so θ = π/4.

The height of the bucket should be the same as the height at whichthe ball exits the launcher. Attach the bucket to the other pole using the clamp and bungee cord ( Figure 2).

Set the launcher and the other pole 4 m apart, at the same horizontal height.

Repeat steps 1.5-1.6 five times and use the average time for calculations.

Notice that the ball reaches a maximum height of 2 meters and stopsinstantaneously when it reaches that height.

The initial position is where the ball exits the launcher.

Launch the ball and use a stopwatch to measure the total time t it takes the ball to reach its maximum height.

Angle the launcher directly upwards so θ = 0.

Use the plunger to place the ball in the launcher at maximum spring tension.

Attach the launcher to a pole, with a 2-m length of pole above it.

Obtain a ball, a launcher with a plunger, two poles, a bucket, two clamps, a bungee cord, and a 2-m stick.

A similar procedure can be done in 1 dimension by shooting the projectile directly upwards, with θ = 0.

Before beginning this experiment, the muzzle velocity of the launcher, 6.3 m/s, is known.These displacement calculations will be compared to the experimental results. If one measures the time it takes for the projectile to complete its path and the angle θ and the initial velocity v 0are known, the displacement in the x- and y-directions can be calculated. Where g is the gravitational acceleration. The two velocity components are v xand v y, where V = v x +v y. A projectile is launched with initial velocity v 0at an angle θ with respect to the x-axis. Y = y 0 + v y,0t + ½ a y t 2 ( Equation 14)įigure 1. X = x 0 + v x,0 t + ½ a xt 2 ( Equation 12) In this coordinate frame, the origin (0,0) corresponds to ( x 0, y 0). Use the equations above to describe this 2-dimensional motion with equations. The velocity in the y-direction reaches a minimum at the peak of the parabola, halfway through the displacement, at t/2, where t is the total time. Therefore, the velocity in the x-direction is constant. The only acceleration the particle experiences is gravity in the negative y-direction. Similarly, in the y-direction, v y,0 = v 0sin (θ). From the figure, one can see that the x-direction component for the initial velocity, v x,0, is v 0cos( θ). Consider a projectile launched with an initial velocity v 0at an angle θ with respect to the x-axis, as shown in Figure 1. These can be expanded to motion in 2 dimensions, x and y, by simply replacing the y components with x components.

Equations 5, 7, 8, and 11 constitute a general set of kinematic equations in the y-direction. Now, motion in 2 dimensions will be considered. These are the useful equations relating position, velocity, acceleration, and time when a is constant. Substituting that t into Equation 6 and again using the definition of Equation 7 again changes the equation for y: T is solved for by substituting Equation 7 into Equation 6:

Substituting this into Equation 6 and using the definition of instantaneous velocity gives a new equation for y: Under constant acceleration, the velocity will increase at uniform rate, so the average velocity will be halfway between the initial and final velocities: Next, calculate the position y as a function of time using Equation 2. Set t 0 = 0 to be the initial time and solve for v in the last equation to obtain the velocity as a function of time: The constant acceleration, a, is the change in velocity divided by the elapsed time: The instantaneous velocity, v, is the velocity over some very small time interval, defined as: The average velocity of the ball, v -, is the displacement divided by the elapsed time: The displacement of the ball, Δ y, is defined as: Denote the initial time as t 0, which corresponds to position y 0. Let's begin by considering the 1-dimensional motion of a ball over some particular time interval t, corresponding to position y. The origin of the coordinate axes (0, 0), will be defined as the initial position of the particle (here, a ball). The x-direction of the coordinate axes will correspond to the horizontal direction, and y to the vertical. Any measurement of the kinematics of an object, such as position, displacement, and speed, must be made with respect to some reference frame.

Projectile motion physics calculator