Up and down motion in free fall – problems and solutions

Solved Problems in Linear Motion – Up and down motion in free fall

1. A person throws a ball upward into the air with an initial velocity of 20 m/s. Calculate how high it goes. Ignore air resistance. Akselerasjon på grunn av tyngdekraften (g) = 10 m/s².

Oppløsning

We use one of these kinematic equations for motion at constant acceleration, som vist under.

v_t = v_o + på

s = v_o t + ½ a t²

v_t² = v_o² + 2 a s

Kjent:

We choose the upward direction as positive and downward direction as negative.

Starthastighet (v_o) = 20 m/s (positive upward)

Acceleration of gravity (g) = – 10 m/s² (negative downward).

Slutthastighet (v_t) = 0 (it’s speed is zero for an instant at highest point)

Ønskes: Maksimal høyde (t)

løsning:

v_t² = v_o² + 2 gh

0 = (20²) + 2(-10) h

0 = 400 – 20 h

400 = 20 h

h = 400 / 20 = 40 / 2 = 20 meters

2. A person throws a stone upward at 20 m/s while standing on the edge of a cliff, so that the stone can fall to the base of the cliff 100 meters below.

(a) How long does it take the ball to reach the base of the cliff (b) Final velocity just before stone strikes the ground. Acceleration due to gravity (g) = 10 m/s². Ignore air resistance.

Kjent:

We choose the upward direction as positive and downward direction as negative.

High (h) = -100 meters (negative because final position below initial position)

Initial hastighet (v_o) = 20 m/s (positive upward)

Tyngdeakselerasjonen (g) = -10 m/s² (negativ nedover)

Ønskes:

(a) Time in air or time interval (t)

(b) Final velocity (v_t)

løsning:

(a) Time interval (t)

Kjent:

High (h) = -100 meters (negative because final position below initial position)

Starthastighet (v_o) = 20 m/s (positive upward), Acceleration of gravity (g) = -10 m/s² (negative downward).

h = v_o t + ½ gt²

-100 = (20) t + ½ (-10) t²

-100 = 20 t – 5 t²

-5t² + 20 t + 100 = 0

We use quadratic formula :

(b) Final velocity

v_t² = v_o² + 2 gh

v_t² = (20²) + 2 (-10)(-100)

v_t² = 400 + 2000

v_t² = 2400

v_t = 49 m/s

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1. Avstand og forskyvning
2. Average speed and average velocity
3. Constant velocity
4. Konstant akselerasjon
5. Fritt fall-bevegelse
6. Down motion in free fall
7. Up and down motion in free fall