Question

use the diagram below, which models a football kicked in projectile motion. what is the vertical component of the balls velocity at point c?
a -9.8m/s²
b -9.8 m/s
c 9.8 m/s²

Explanation:

Step1: Analyze projectile motion at highest point

In projectile motion, at the highest point (point C here), the vertical component of velocity is \(0\). But let's check the options. Option A and C have units of \(m/s^{2}\) which is acceleration (\(g = 9.8m/s^{2}\) is acceleration due to gravity). We are asked for velocity. Velocity has units of \(m/s\). At the highest point of projectile motion, the vertical component of velocity is moment - arily \(0\). But if we consider the options given, maybe there is a mis - understanding. Wait, no, another approach: the vertical component of velocity \(v_y=v_{0y}-gt\). At the highest point, the time to reach the highest point \(t = \frac{v_{0y}}{g}\), so \(v_y = 0\). But looking at the options again, perhaps it's a trick question. Wait, no, actually, if we consider the general formula for vertical velocity \(v_y\) in projectile motion \(v_y = v_{0}\sin\theta - gt\). At the peak (point C), the vertical velocity \(v_y = 0\). But among the given options, if we assume a wrong - concept check (maybe confusion between acceleration and velocity). Acceleration \(a=-g=- 9.8m/s^{2}\) (downward, so negative). Velocity: at point C (highest point) vertical velocity \(v_y = 0\). But since \(0\) is not an option, and considering units: options A and C are accelerations (units \(m/s^{2}\)), option B is velocity (unit \(m/s\)). Maybe the question has an error. But if we go by elimination (units first): we need velocity (unit \(m/s\)). So options A and C are wrong (units \(m/s^{2}\)).

Answer:

Since we need a velocity (unit \(m/s\)), and options A and C have wrong units (\(m/s^{2}\)), but if we assume a mis - print (maybe they thought of acceleration as velocity, but strictly by units) there is no correct option. But if we consider the closest (by unit), and if there was a mis - take in the problem (maybe they wanted to ask about acceleration at some point, but if we have to choose from given options based on unit: B (though conceptually at point C vertical velocity is \(0\), but units matter here). So B. Option B.