Question

a ball is kicked from the ground at an angle so that its initial velocity has components ($v_x = 10 m/s$, $v_y = 20 m/s$). the ball is kicked over flat, horizontal ground. ignore the effects of air resistance. what is the horizontal displacement of the ball while it is in the air?
a 10 m
b 20 m
c 40 m
d 80 m

Explanation:

Step1: Find the time of flight

Use the vertical motion equation \(y = v_{y}t-\frac{1}{2}gt^{2}\). Since the ball starts and ends at \(y = 0\) (ground level), \(0 = 20t - 5t^{2}\) (taking \(g = 10m/s^{2}\)). Factor out \(t\): \(t(20 - 5t)=0\). Solutions are \(t = 0\) (initial time) and \(t=\frac{20}{5}=4s\).

Step2: Calculate the horizontal displacement

Use the horizontal motion equation \(x=v_{x}t\). Given \(v_{x}=10m/s\) and \(t = 4s\), then \(x=10\times4 = 40m\).

Answer:

C. 40 m