Question

analyzing projectile motion
the table represents the height in meters of a baseball a pitcher threw to another player after a certain number of seconds. what are the missing values in the table?
time (seconds) height (meters)
0 0
1 24.5
2 39.2
3 44.1
4 39.2
5 a
6 b

Explanation:

Step1: Identify the pattern of height - time relationship

The height of a projectile motion can be modeled by a quadratic function. The general form of the height - time function for vertical motion under gravity is $h(t)=v_0t-\frac{1}{2}gt^2$, where $v_0$ is the initial velocity and $g = 9.8m/s^2$. We can also observe the symmetry of the projectile motion. The motion is symmetric about the vertex of the parabolic path. The maximum height occurs at the vertex. Here, the maximum height is at $t = 3$ seconds.

Step2: Use the symmetry of projectile motion

Since the motion is symmetric about $t = 3$ seconds, the height at $t=1$ second is the same as the height at $t = 5$ seconds, and the height at $t=2$ seconds is the same as the height at $t = 4$ seconds. Also, at $t = 0$ and $t=6$ seconds, the height is 0 (assuming the ball returns to the same height from which it was thrown).

Answer:

A = 24.5
B = 0