Question

A ball is thrown upward with a velocity 40m/s. Fend it's velocity and height after 2sec.

Answer 1

Answer :

• Velocity after 2 seconds is 20 m/s.
• Height after 2 seconds is 60 m.

Given Information :

• Initial velocity (u) = 40 m/s

• Time (t) = 2 s

To calculate :

• Velocity after 2 seconds (v)

• Height after 2 seconds (h)

Calculation :

$\underline{\small \sf {\maltese \; \; \; Finding \: its \: velocity \: after \: 2 \: seconds \: (v) : \; \; \; }}$

By using the first equation of motion for frèély falling bodies,

$\longrightarrow \boxed{ \sf {v = u + gt} }$

• v denotes final velocity
• u denotes initial velocity
• g denotes acceleration due to gravity
• t denotes time

[Value of g is taken as 10 m/s².]

Note : Here, g will be negative since it has been thrown in upward direction.

$\longrightarrow \sf {v = 40 + ( -10 \times 2) }$

$\longrightarrow \sf {v = 40 + (-20)}$

$\longrightarrow \sf {v = 40 -20 }$

$\longrightarrow \sf\red {v = 20 \: m/s}$

Therefore, velocity after two seconds is 20 m/s.

$\underline{\small \sf {\maltese \; \; \; Finding \: its \: height \: after \: 2 \: seconds \: (h) : \; \; \; }}$

By using the second equation of motion for frèély falling bodies,

$\longrightarrow \boxed{ \sf {h = ut + \dfrac{1}{2}gt^2} }$

• h denotes height
• u denotes initial velocity
• g denotes acceleration due to gravity
• t denotes time

g = –10 m/s²

$\longrightarrow \sf {h = 40(2) + \dfrac{1}{2}\times (-10) \times (2)^2 }$

$\longrightarrow \sf {h = 80 + \dfrac{1}{2}\times (-10) \times 4 }$

$\longrightarrow \sf {h = 80 + (-10) \times 2 }$

$\longrightarrow \sf {h = 80 + (-20) }$

$\longrightarrow \sf {h = 80 -20 }$

$\longrightarrow \sf \red{h = 60 \: m}$

Therefore, height after 2sec is 60 m.

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★ Points to remember :

Equations of motion for frèély falling bodies :

• v = u + gt
• h = ut + ½gt²
• v² = u² + 2gh

Where,

• v denotes final velocity

• u denotes initial velocity

• g denotes acceleration due to gravity

• h denotes height

• t denotes time

Answer 2

u = + 40 m/s

t = 2 s

g = - 10 m/s²

We know:-

v = u + gt

⇒ v = 40 m/s + 2 s(- 10 m/s²)

⇒ v = 40 m/s - 20 m/s

⇒ v = 20 m/s

Now, 2ax = v² - u²

⇒ x = (v² - u²)/2a = (400 - 1600)/(- 20 m)

⇒ x = 1200/20 m = 60 m.

So, the velocity of it after 2 seconds in 20 m/s and it will be elevated to a height of 60 m.

More:-

• dv = dx/dt
• v = u + at
• 2ax = v² - u²
• x = ut + ½ gt².