A Magenta ball is dropped from a 70m tall building. One second later, a Cyan col

Question

A Magenta ball is dropped from a 70m tall building. One second later, a Cyan colored ball is thrown downward at 20m/s. (A.) How long does it take for the Cyan ball to catch up to the magenta ball? (B.) How high above the ground are they when they meet? (C.) What is the velocity of the Magenta ball at that moment? (D.) What is the velocity of the Cyan ball when they meet? A Magenta ball is dropped from a 70m tall building. One second later, a Cyan colored ball is thrown downward at 20m/s. (A.) How long does it take for the Cyan ball to catch up to the magenta ball? (B.) How high above the ground are they when they meet? (C.) What is the velocity of the Magenta ball at that moment? (D.) What is the velocity of the Cyan ball when they meet? A Magenta ball is dropped from a 70m tall building. One second later, a Cyan colored ball is thrown downward at 20m/s. (A.) How long does it take for the Cyan ball to catch up to the magenta ball? (B.) How high above the ground are they when they meet? (C.) What is the velocity of the Magenta ball at that moment? (D.) What is the velocity of the Cyan ball when they meet?

Explanation / Answer

Let the balls meet after time t

distance after which the ball meets be S

it will be the same for both the balls

S = ut + 0.5gt^2 = 0.5*9.8*t^2 for magenta ball ---------(1)

S = 20(t-1) + 0.5*9.8*(t-1)^2 for Cyan ball ------(2)

4.9t^2 = 20(t-1) + 4.9(t-1)^2

4.9t^2 = 20t - 20 + 4.9t^2 + 4.9 - 9.8t

10.2t -15.1 = 0

A) t = 1.48 s

B)S = 4.9t^2= 4.9*(1.48^2) = 10.73 m

70 - 10.73 = 59.26 m

C) v = u +at

v = 0 + 9.8*1.48 = 14.504 m/s

D) v = u + at

= 20 + 9.8*1.48 = 34.504 m/s

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