Motus deorsum in casu libero – problemata et solutiones

Solved Problems in Linear Motion – Down motion in free fall

1. A ball is thrown vertically downward with initial speed 10 m/s and reach the ground in 2 seconds. Find final speed just before the ball hits the ground. Acceleratio gravitatis (g) = 10 m/s²Resistentiam aeris neglege.

Notum:

Velocitas initialis (v_o) = 10m/s

Time elapsed (t) = 2 seconds

Acceleratio gravitatis (g) = 10 m/s²

Wanted : Final velocity (v_t)

solution:

Acceleratio 10 m/s² means speed increase by 10 m/s each second. After 3 second, speed = 30 m/s.

Final velocity = 10 m/s + 20 m/s = 30 m/s.

Kinematic equations for motus cum acceleratione constanti, as shown below :

v_t v =_o + a t ………. 1

h = v_o t + ½ apud² ………. 2

v_t² v =_o² + 2 a h ………. 3

v_t v =_o + gt

v_t = 10 + (10)(2)

v_t = 10 + 20 = 30 m/s

Final velocity = v_t = 30m/s

2. A stone is thrown vertically downward from a bridge with initial speed 5 m/s and reach the water in 2 seconds. Calculate the height of the bridge.

Notum:

Velocitas initialis (v_o) = 5m/s

Time elapsed (t) = 2 seconds

Acceleratio gravitatis (g) = 10 m/s²

Quaesitum: the height of the bridge (h)

solution:

h = v_o t + ½ gt²

h = (5)(2) + ½ (10)(2)²

h = 10 + (5)(4)

h = 10 + 20

h = 30 metra

3. A ball is thrown vertically downward with initial speed 10 m/s from a height of 80 meters. Find (a) Time in air (b) Final velocity just before ball strikes the ground.

Notum:

height (h) = 80 meters

Velocitas initialis (v_o) = 10m/s

Acceleratio gravitatis (g) = 10 m/s²

Quaesitum:

(a) Intervallum temporis (t)

(b) Velocitas finalis (v)_t)

solution:

(a) Intervallum temporis (t)

Final velocity :

v_t² v =_o² + 2 gh

v_t² = (10)² + 2(10)(80) = 100 + 1600 = 1700

v_t = 41m/s

Time interval (t) :

v_t v =_o + gt

41 = 10 + (10)(t)

41 – 10 = 10 t

31 = 10 t

t = 31 / 10 = 3,1 secunda

(b) Velocitas finalis (v)_t) ?

v_t = 41m/s

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1. Distantia et dislocatio
2. Celeritas media et velocitas media
3. Velocitas constans
4. accelerationis constant
5. Motus casus liberi
6. Motus deorsum in casu libero
7. Motus sursum deorsumque in casu libero