Answer:
1) v(t=2s) = - 64 ft/s
2) vf= 78.4 ft/s
Explanation:
height of the ball as a function of time
h= f(t) = 96 − 16t² ft Equation (1)
Instantaneous velocity of the ball t = 2 seconds after it is dropped
v=dh/dt=-32 t Equation (2): Instantaneous velocity
v(t=2s)= -32*2 = -64 ft/s
Speed of the ball when it hits the ground
When the ball hits the ground , h=0 , then, We replace data in the equation (1) to calculate the time it takes for the ball to touch the ground
h = 96 − 16t²
0 = 96 − 16t²
16t² = 96
t² = 96 /16 =6
[tex]t= (\sqrt{6} ) s[/tex]
t = 2,45 s
We apply the kinematic equation of the ball in free fall
vf= v₀+gt Formula (1)
Where:
t : time in seconds (s)
v₀: initial speed in ft/s
vf: final speed in ft/s
g: acceleration due to gravity in ft/s²
Data
v₀= 0
t = 2,45 s
g = 32 ft/s²
We replace data in the formula (1)
vf= v₀+gt
vf= 0+ (32)(2,45)
vf= 78.4 ft/s
