A blue ball is thrown upward with an initial speed of 20.8 m/s, from a height of

Question

A blue ball is thrown upward with an initial speed of 20.8 m/s, from a height of 0.6 meters above the ground. 2.5 seconds after the blue ball is thrown, a red ball is thrown down with an initial speed of 10.4 m/s from a height of 24.6 meters above the ground. The force of gravity due to the earth results in the balls each having a constant downward acceleration of 9.81 m/s2.

How long after the blue ball is thrown are the two balls in the air at the same height?

Which statement is true about the blue ball after it has reached its maximum height and is falling back down?

The acceleration is positive and it is speeding up

The acceleration is negative and it is speeding up

The acceleration is positive and it is slowing down

The acceleration is negative and it is slowing down

Explanation / Answer

(1) for blue ball , Yb= Yo+Vot+1/2 at2

Yb=0.6+20.8t+1/2 (-9.8)t2

Yb=0.6+20.8t-4.9t2

for red ball;

Yr=24.6-(10.4(t-2.5)+1/2 (9.8)(t-2.5)2)

Yr=24.6-10.4t+26-4.9(t2-5t+6.25)

Yr=19.975+14.1t-4.9t2

now Yr= Yb

19.975+14.1t-4.9t2=0.6+20.8t-4.9t2

19.975+14.1t=0.6+20.8t

t=2.89s

(b) The acceleration is negative and it is speeding up

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