This problem asks us to calculate the vertical and horizontal distance the dart travels, given the initial velocity (10 m/s horizontally) of the throw and time of flight (0.19 s).
For projectile motion problems in general, we'll follow these steps to solve:
- Identify the target variable and known variables for each direction—remember that only 3 of the 5 variables (Δx or Δy, v0, vf, a, and t) are needed for each direction. Also, it always helps to sketch out the problem and label all your known information!
- Choose a UAM equation—sometimes you'll be able to go directly for the target variable, sometimes another step will be needed in between.
- Solve the equation for the target (or intermediate) variable, then substitute known values and calculate the answer.
The four UAM (kinematics) equations are:
We define our coordinate system so that the +y-axis is pointing upwards and the +x-direction is horizontal along the launch direction. That means ay = −g, and ax = 0 (because after a projectile is launched, the only acceleration is due to gravity.)
For a horizontally launched projectile, we also know that v0y = 0.