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Ari and Matthew are both running toward the soccer ball during a game.

Ari's path is represented by the parametric equations x(t)=36+1/6t, y(t)=24+1/8t, where t is on the interval [0,50] and t is measured in tenths of seconds.

Matthew's path is represented by the parametric equations x(t)=32+1/4t, y(t)=18+1/4t, where t is on the interval [0,50] and t is measured in tenths of seconds.

Do the boys collide? If so, when do they collide?

Ari and Matthew collide at 3.2 seconds.

Ari and Matthew collide at 4.8 seconds.

Ari and Matthew collide at 2.4 seconds.

Ari and Matthew do not collide.

 May 18, 2020
 #1
avatar+26009 
+1

Set the y equations equal

24+ 1/8 t = 18+ 1/4 t      solve to find t = 48    (4.8 seconds)

 

Sub this value into the x equations ......if the results are equal a collision happens at  4. 8 sec

 May 19, 2020

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