physics homework question

Question

A ball is thrown directly downward with an initial speed of 7.95 m/s, from a height of 30.2 m. After what time interval does it strike the ground?

Answer 1

1. Identify the type of problem. Since the ball falls downward under the influence of gravity, and since it has a symmetrical shape that allows you ignore air resistance → This is a free fall problem. Since there is no mention of mass or energy, this would be a pure 1D kinematics problem.
2. List givens and unknowns to help you select the correct equation.
3. Note that some values are implied by their wording (ex. "dropped" or "released" means that v_iy = 0 m/s). In this example, the phrase "strikes the ground" indicates that y_f = 0.0 m. Given: v_yi = -7.95 m/s, ay = -g = -9.81 m/s², y_i = 30.2 m, and y_f = 0.0 m. Find: t. (I took down as the negative direction.)
4. Since time is involved but not final velocity, this suggests that the best equation would be that for 1D motion that depends on time: y_f = y_i + v_iyt + (1/2)a_yt². If you have trouble chossing the correct one, don't worry! It's okay to try two equations and see which one gives the least # unknowns. Of course, if you end up with only 1 unknown, then you would solve that one, but sometimes you need 2 equations to solve for 2 unknowns.
5. Substitution and Algebraic Manipulation → Include units!:
6. y_f = y_i + v_iyt + (1/2)a_yt²
7. → 0 m = 30.2 m - (7.95 m/s)t -(1/2)(9.81 m/s²)t²
8. This does indeed give us only one unknown, t, which is what we're solving for. You would then proceed with the quadratic equation to solve for t. Remember to take only the positive root!