Aball player catches a ball 3.13 s after throwing it vertically upward. a)with what speed did he throw it?
b)what height did it reach?

a) v₀ = 15.3 m/s

b) h = 11.9 m

Explanation:

Ball Kinematics

We apply the free fall formulas:

vf= v₀+at Formula (1)

vf²=v₀²+2*a*y Formula (2)

y= v₀t+ (1/2)*a*t² Formula (3)

y:displacement in meters (m)  

v₀: initial speed in m/s  

f: final speed in m/s  

a: acceleration in m/s²  

Data

t= 3.13 s

a=g= -9.8 m/s² = acceleration due to gravity

Problem development

a)With what speed did he throw it

We apply the formula (1) for calculate initial speed (v₀)

vf= v₀+at

0=  v₀+(-9.8)*(3.13/2)

v₀= 15.3 m/s

b)What height did it reach?

We apply formula (2) or formula (3)

vf²=v₀²+2*a*h formula (2)

0 = v₀² +2*(-9.8)*h

19.6*h =  v₀²

h=v₀²/19.6

h= (15.3)²/(19.6 )

h= 11.9m

y= v₀t+ (1/2)*a*t² Formula (3)

h= (15.3)(3.13/2)+(1/2)(-9.8)(3.13/2)²= 11.9m

the assestment will probley apele with cause and effect

that tool is called an altimeter which measures your altitude which can be used to tell which atmosphere you are currently in, including the stratosphere.

hope this ! : )