Average Velocity and Instantaneous Velocity, Projectile Motion Analyzed?

Question

A soccer ball is kicked from the ground with an initial speed of 20.8 m/s at an upward angle of 48.0°. A player 40.6 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground? Neglect air resistance.

Answer 1

The equations for this are:

Ball
x(t)=20.8*cos(48)*t
player
x(t)=40.6-v*t

To find when the ball will return to the ground, find the time to apogee and double it
vy(t)=0=20.8*sin(48)-g*t
t=20.8*sin(48)/g
using g=9.81
t=0.753 seconds
so the flight time
1.506 seconds
so x(t)=20.8*cos(48)*1.506
29.28 meters
given that
29.28=40.6-v*1.506
v=7.517 m/s

j

Answer 2

average velocity is calculated over a quantity of time. case in point, permit's say the preliminary place is 0 meters. the perfect place is twenty meters. If it took 5 seconds to trip twenty meters, then the final velocity is 4 meters consistent with 2nd. on the spot velocity is calculated at an occasion of time. An occasion could be calculating the speed at twenty-one meters at a time of precisely 3 seconds. The on the spot velocity could be seven meters consistent with 2nd. In the two circumstances, derivatives and/or limits could be used to make velocity calculations.