- #1

cmonstre

- 1

- 0

**Hi! I'm working on a problem for class and am having trouble figuring out how to calculate the initial velocity, which I need in order to calculate acceleration and from there the value of an unknown force. I thought I was on the right track, but my professor reminded me that I need to use the instantaneous initial velocity, not the average velocity. The problem is below:**

1. Homework Statement

1. Homework Statement

A 0.15kg object is launched from the ground and moves under the influence of gravity as well as a second force (wind). The wind force is constant, but magnitude and direction are unknown. We are given a table of values (points) from the plot of the trajectory and are asked to calculate the force of the wind on the ball.

The table looks like this:

t(s), x(m), y(m)

t=0, x=0, y=0

t=.5, x=3.46, y=4.59

t=1, x=6.72, y=6.85

t=1.5, x=9.81, y=6.79

t=2, x=12.70, y=4.40

The graph is obviously a parabola.

## Homework Equations

I'll put the kinematic equations down for reference:

deltax= 1/2 (V

_{f}- V

_{0})t

deltax = V

_{f}t - 1/2at

^{2}

deltax= V

_{0}t + 1/2at

^{2}

V

_{f}- V

_{0}= at

Vf

^{2}= V0

^{2}+ 2a(deltax)

## The Attempt at a Solution

Alright. I know that the values in the table can give me information to calculate displacement, instantaneous velocities, and time, from which I can calculate acceleration using the kinematic equations. Since I also know the mass of the object, I can then use the F=ma equation to calculate the force of the wind.

I know that if the force on an object is constant, the acceleration must be constant (because the mass is obviously constant)…so the acceleration of the object wouldn't change across the trajectory. I think this means that the vertical acceleration (Ay) would be the acceleration due to gravity PLUS the acceleration of the wind, and the horizontal acceleration (Ax) would just be the acceleration of the wind. Unless of course the wind acceleration only affects the horizontal acceleration, and then the vertical acceleration is just acceleration due to gravity.

My original thought process was to calculate initial horizontal velocity, and then calculate acceleration from there. The issue I ran into is that using the values from the table only gave me average velocity across that interval. Then I thought that I could solve for the angle of launch for a better approximation of V0.

I used the x value of 6.72m and the y value of 6.85m, then used tan(theta)=6.85/6.72 to solve for the launch angle, which gave me approximately 45.5 degrees. The initial horizontal velocity would then be V0x= V0*cos(45.5), and the initial vertical velocity would be V0y=V0*sin(45.5). My professor stopped me here and reminded me that this is still an approximation though and told me to construct a system of equations that would allow me to solve for the exact initial velocity. I'm not sure where to start with the system of equations, because I only have the displacement and time variables as I would run into the same issue of having an average velocity if I tried to calculate Vf.

Once I have the value for initial velocity, however, I would be able to solve for acceleration using

deltax= V

_{0}t + 1/2at

^{2}

and then multiply the acceleration by the mass of the projectile to get Fx. From there it would just be solving for the unknown force.

Thanks for the help! I know this is ultimately pretty basic, but this is my first physics class!