A student standing on the ground throws a ball straight up. The ball leaves the student's hand with a speed of 17.0 m/s when the hand is 1.50 m above the ground. How long is the ball in the air before it hits the ground? (The student moves her hand out of the way.)

The ball is 3.16 seconds in the air before it hits the ground.

Explanation:

Upward:

v = v o - g t

0 m/s = 15 m/s - 9.81 m/s² · t

15 m/s = 9.81 m/s² · t

t = 15 m/s : 9.81 m/s²

t 1 = 1.53 s

h = v o · t - g t² / 2  + 2 m

h = 22.95 m - (9.81 m/s² · 2.3409 s²) / 2 + 2 m

h = 11.475 m + 2 m = 13.475 m

Downward:

13.475 m = 9.81 · t² / 2

t = √(13.475 · 2 ) / 9.81

t 2 = 1.66 s

t = t 1 + t 2 = 1.53 s + 1.66 s = 3.19 s

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.