A soccer ball is kicked with an initial velocity of 25.0 ms and at an angle of 3

Question

A soccer ball is kicked with an initial velocity of 25.0 ms and at an angle of 30.0 with respect to the horizontal. The ball crosses the goal line as it lands. Fill the table with the information you know, or write a simple expression for it (see example), specify that which you do not know with a symbol. Then make a drawing showing the trajectory of the ball and of the situation. Using the information you collected, find the time the ball spends in the air. Using the time of flight, calculate the total horizontal distance the travelled.

Explanation / Answer

vo = 25 m/s, theta = 30 degrees

(I) xo = 0

x = 25*cos(30)*t= 21.65*t

vox = 25*Cos(30) =21.65 m/s

vx = vox = 21.65 m/s

ax = 0

yo =0

y = voy*t +(1/2)at^2

y = 25*Sin(30)t -(1/2)9.8*t^2

y= 12.5*t - 4.9t^2

voy = 25*sin(30) = 12.5 m/s

vy = voy+gt

vy = 12.5 -9.8*t

ay = -9.8 m/s^2

(II) Time of flight T = 2*vo*sin^(theta)/g

T = 2*25*sin(30)/(9.8)

T = 2.55 s

(III) R = vox*T

R = 25*cos(30)*2.55

R = 55.2 m

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