A soccer ball is kicked at an angle of 20 degrees. It lands on the ground 26 meters away from it starting point. What is the initial speed of the ball?

Answer 1

Initially, the x & y components of the initial velocity are v_ox & v_oy in terms of the initial velocity v_o

Based on the kick angle, v_ox = v_ocos(20) = .94v_o and v_oy = v_osin(20) = .342v_o

Using the basic equation of height for the y component, you will find that that the time to reach the maximum height will be v_o/g (g = acceleration due to gravity = 9.8 m/s²) and the maximum height will be (.5)v²_oy/g

the time for the ball to go up & come down is twice that number =2v_oy/g = 2(.342v_o)/9.8 = .07v_o

Now that we know the total time to return to earth, we look to the x coordinate. We know that the x direction velocity is v_ox = .94v_o

So, distance (x) = v_ox(time) = (.94v_o)(.07v_o) = 26 meters (The x direction velocity is constant)

Solving for v_o we find that v_o = 19.9 meters (the initial velocity of the kick)