Calculating the tangential component of the force acting on a projectile

[kylera]

Homework Statement

Consider a projectile launched horizontally out the window of a tall building at a speed v(0). Determine an expression for the tangential component of the force acting on the projectile in terms of m, g, t, and v(0). Assume that the air has a negligible effect on the motion.

Homework Equations

F = ma, mostly deductions.

The Attempt at a Solution

V(h) = the horizontal velocity = v(0)
V(v) = the vertical velocity = mt

From here, I assume that since the horizontal velocity does not change because of negligible air resistance, F(h) = horizontal element of the total force applied on the projectile = zero. F(v) = mass * gravity = mg. However, this brings me to where I'm stuck -- I can't figure out how to determine the angle at which the projectile is falling. It can't be straight down. Do I find the angle using the velocities instead and then apply it to the force?

 

[tiny-tim]

From here, I assume that since the horizontal velocity does not change because of negligible air resistance, F(h) = horizontal element of the total force applied on the projectile = zero. F(v) = mass * gravity = mg. However, this brings me to where I'm stuck -- I can't figure out how to determine the angle at which the projectile is falling. It can't be straight down. Do I find the angle using the velocities instead and then apply it to the force?

Hi kylera!

Yes, the angle changes with t …

so find the horizontal and vertical components of the velocity as a function of t.

 

[kylera]

Done! Thanks!