Question

A soccer ball is kicked in such a manner that the x and y components of...

A soccer ball is kicked in such a manner that the x and y components of its position at any time are given by

x = (19.6 m/s)t

and

y = (14.5 m/s)t − (4.90 m/s2)t2,

where x and y will be in meters when t is in seconds.

(a) Determine expressions for the x and y components of its velocity at any time. (Use the following as necessary: t.)

vx

=   m/s

vy

=   m/s


(b) Determine expressions for the x and y components of its acceleration at any time. (Use the following as necessary: t.)

ax

=   m/s2

ay

=   m/s2


(c) Determine expressions for the position, velocity, and acceleration vectors of the ball at the time

t = 1.73 s.

(Express your answer in vector form.)

r(t = 1.73 s)

 =   m

v(t = 1.73 s)

 =   m/s

a(t = 1.73 s)

 =   m/s2
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Answer #1

Differentiate the position to find velocity and differentiate the velocity to find the acceleration as shown below

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