A ball thrown thrown vertically upwards with the velocity 20 m/s. calculate how high it goes

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Explanation:

Question:

A ball is thrown vertically upwards with a velocity of 20ms^-1 from the top of a multistorey building. The height of the point from where the ball is thrown is 25.0m from the ground.

(a) How high will the ball rise?

(b) how long will it be before the ball hits the ground?

Solution:

(a) Here,

u = + 20 m/s

g = - 10 m/s²

At the highest point, v = 0

Suppose the balls rise to the highest h from the point of projection.

v² - u² = 2gs

⇒ (0)² - (20)² = 2 × (- 10) × h

⇒ h = + 20 m.

Hence, the ball rises to 20 m.

(ii) Net displacement, s = - 25 m.

Negative sign is taken because displacement is in the opposite direction of the initial velocity.

s = ut + 12 gt²

⇒ - 25 = 20t + 1/2 × (- 10) × t²

⇒ 5t² - 20t - 25 = 0

⇒ t² - 4t - 5 = 0

⇒ (t + 1) (t - 5) = 0

⇒ t ≠ - 1, 5 seconds

⇒ t = 5 seconds.

Hence, the ball hits the ground to 5 seconds.