Two students are on a balcony 19.9 mabove the street. One student throws a ball

Question

Two students are on a balcony 19.9 mabove the street. One student throws a ball (ball 1) verticallydownward at 13.9 m/s; at the sameinstant, the other student throws a ball (ball 2) vertically upwardat the same speed. The second ball just misses the balcony on theway down. (a) What is the difference in the two ball'stime in the air?
1 s

(b) What is the velocity of each ball as it strikes the ground? ball 1 magnitude 2 m/s direction 3---Select---upwarddownward ball 2 magnitude 4 m/s direction 5---Select---upwarddownward
(c) How far apart are the balls 0.500s after they are thrown?
6 m (a) What is the difference in the two ball'stime in the air?
1 s

(b) What is the velocity of each ball as it strikes the ground? ball 1 magnitude 2 m/s direction 3---Select---upwarddownward ball 2 magnitude 4 m/s direction 5---Select---upwarddownward
(c) How far apart are the balls 0.500s after they are thrown?
6 m ball 1 magnitude 2 m/s direction 3---Select---upwarddownward ball 2 magnitude 4 m/s direction 5---Select---upwarddownward

Explanation / Answer

height of balcony h = 19.9 m speed of the ball v = 13.9 m / s (a). the difference in the two ball's time in the air T = t +t ' where t = time taken to the ball (which is thrown upward) to reach maximum height              = v / g              = 1.418 s            t' = time taken to the ball to reach balcony from maximumheight               = v / g = 1.418 s therefore T = 2.836 s (b).velocity of the ball 1 when it hits the ground V = v+ gt " where t " = time taken to the ball 1 to reach theground from the relation h = vt +( 1/ 2) gt ^ 2                        19.9=13.9 t + 4.9 t^ 2 4.9 t^2 + 13.9 t - 19.9 = 0 t = { -13.9 ± [13.9^ 2 -(4*4.9*-19.9) }/ ( 2*4.9)     = { -13.9 ± 24.15 } / 9.8    = 1.0459 s     Since time isnot negative value Therefore V = 13.9 + (9.8* 1.0459 )                     = 24.15 m / s direction down ward velocity of the ball2 when it hits the ground =24.15 m / s direction downward   Since both thrown with samespeed ( offcourse one is up and one is down)

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