Kuyenda pansi mu kugwa kwaulere - mavuto ndi mayankho

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. Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²Musanyalanyaze kukana kwa mpweya.

Zodziwika:

Liwiro loyambirira (v)_o) = 10 m/s

Time elapsed (t) = 2 seconds

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

Wanted : Final velocity (v_t)

Yankho:

Kuthamanga 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 kuyenda mofulumira nthawi zonse, as shown below :

v_t =v_o + a t ………. 1

h = v_o t + ½ pa² ………. 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 = 30 m/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.

Zodziwika:

Liwiro loyambirira (v)_o) = 5 m/s

Time elapsed (t) = 2 seconds

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

Akufuna: the height of the bridge (h)

Yankho:

h = v_o t + ½ gt²

h = (5)(2) + ½ (10)(2)²

h = 10 + (5)(4)

h = 10 + 20

h = mamita 30

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.

Zodziwika:

height (h) = 80 meters

Liwiro loyambirira (v)_o) = 10 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

Akufuna:

(a) Nthawi yopuma (t)

(b) Liwiro lomaliza (v)_t)

Yankho:

(a) Nthawi yopuma (t)

Final velocity :

v_t² =v_o² + 2 gh

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

v_t = 41 m/s

Time interval (t) :

v_t =v_o + gt

41 = 10 + (10)(t)

41 – 10 = 10 t

31 = 10 t

t = 31 / 10 = masekondi awiri

(b) Liwiro lomaliza (v)_t) ?

v_t = 41 m/s

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3. Liwiro lokhazikika
4. Kuthamanga kosalekeza
5. Kuyenda kwaulere kwa kugwa
6. Kuyenda pansi mu kugwa kwaulere
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