Physics: From the top of 100m tall building you throw a ball upward with a speed of 10 m/s.?

1.
Take g = 9.81 m/s²
Take all downward quantities as positive.

a)
Initial velocity, vₒ = -10 m/s
Acceleration, a = 9.81 m/s²
Final velocity, v = 0 m/s

v = vₒ + at
0 = -10 + 9.81t
Time taken, s = 1.0 s

b)
Initial velocity, vₒ = -10 m/s
Acceleration, a = 9.81 m/s²
Final velocity, v = 0 m/s

v² = vₒ² + 2as
0 = (-10)² + 2(9.81)s
s = -5.1
Max. height above the ground = (100 + 5.1) m = 105.1 m

c)
Initial velocity, vₒ = -10 m/s
Acceleration, a = 9.81 m/s²
Displacement, s = 100 m

s = vₒt + (1/2)at²
100 = (-10)t + (1/2)(9.81)t²
4.905t² - 10t - 100 = 0
t = [10 + √(10² - 4×4.905×100)] / (2×4.905)
Time taken, t = 5.6 s

d)
Initial velocity, vₒ = -10 m/s
Acceleration, a = 9.81 m/s²
Displacement, s = 100 m

v² = vₒ² + 2as
v² = (-10)² + 2(9.81)(100)
v = √[(-10)² + 2(9.81)(100)]
Final velocity, v = 45 m/s

a) t = v/g = 10/9.8 = 1.02 s

b) h = v²/2g
h = 10²/2•9.8 = 5.10 m
add 100 to get 105 m

c) time to fall 105.1 m
t = √(2h/g)
t = √(2•105/9.8) = 4.63 s
add to that 1.02 s for upward time to get 5.65 s

d) v = √(2gh)
v = √(2•105•9.8) = 44.7 m/s





falling object starting from rest (and reverse)
h is height in meters, t is time falling in seconds,
g is acceleration of gravity, usually 9.8 m/s²
v is velocity in m/s
h = ½gt²
t = √(2h/g)
v = √(2gh)
h = v²/2g
v = gt