Question

a ball is kicked from the ground at an angle so that its initial velocity has components (vx = 10 m/s, vy = 20 m/s). the ball is kicked over flat, horizontal ground. ignore the effects of air resistance. how long will the ball be in the air before hitting the ground? a 1 sec b 2 sec c 4 sec d 8 sec

Explanation:

Step1: Analyze vertical motion

The vertical displacement formula for projectile motion is \(y = v_{y}t-\frac{1}{2}gt^{2}\). When the ball hits the ground, \(y = 0\). Given \(v_{y}=20\ m/s\) and \(g = 10\ m/s^{2}\), the equation becomes \(0=20t - 5t^{2}\).

Step2: Solve the quadratic equation

Factor out \(t\): \(t(20 - 5t)=0\). This gives two solutions: \(t = 0\) (initial time when the ball is kicked) and \(20-5t=0\). Solving \(20-5t = 0\) for \(t\), we get \(t=\frac{20}{5}=4\ s\).

Answer:

C. 4 sec