Question

$\LARGE{\color{red}{\textsf{\textbf{ Question }}}}$
A ball is thrown vertically upwards with a velocity of 49 m/s.

Calculate
(i) The maximum height to which it rises,

(ii) The total time it takes to return to the surface of the earth.

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Answer 1

$\LARGE{{\textsf{\textbf{ Question - }}}}$

A ball is thrown vertically upwards with a velocity of 49 m/s.

Calculate

(i) The maximum height to which it rises,

(ii) The total time it takes to return to the surface of the earth.

$\LARGE{{\textsf{\textbf{ Answer - }}}}$

Given -

• Initial velocity (u) = 49m/s.

• Final Velocity (v) = 0

• Gravity = 9.8 m/s²

To Find -

• The maximum height to which it rises.

• The total time it takes to return to the surface of the earth.

Solution -

Answer (1)

• g = Gravity
• h = height
• v = final velocity
• u = initial velocity

Formula

$\sf{ 2gH = {v}^{2} – {u}^{2} }$

After putting the values ,

• g = -9.8
• h = (to find)
• v = 0
• u = 49

$: \Longrightarrow\sf{2 × (- 9.8) × h = {0}^{2} - {49}^{2} }$

$: \Longrightarrow\sf{– 19.6 × h = {0}- 2401 }$

$: \Longrightarrow\sf{– 19.6 h = - 2401 }$

$: \Longrightarrow\sf{ h = \dfrac{2401}{ 19.6 } }$

$: \Longrightarrow\sf{ h = 122.5 \: m }$

Answer (2)

• g = Gravity
• t = time
• v = final velocity
• u = initial velocity

Formula

$\sf{ v = u + g \times t }$

After putting the values ,

• g = -9.8
• t = (to find)
• v = 0
• u = 49

$: \Longrightarrow\sf{ 0 = 49 + (- 9.8) × t}$

$: \Longrightarrow\sf{ t = 5 sec}$

The total time ball takes to return to the surface of the earth = 2t

$: \Longrightarrow\sf{ 2 \times 5= 10 sec}$