Question

The object dropped from a height (h) with initial velocity zero strikes the ground with a velocity of 30m's.
How long does it take to reach the ground. Also find h lg = 10m/s)​

Answer 1

Given -

• Initial velocity (u) = 0 m/s
• Final velocity (v) = 30 m/s
• Acceleration due to gravity (g) = $\sf{10~m/s^2}$

To find -

• Time the object will take to reach the ground.
• Height.

Solution -

• v = u + at

Substitute the given values -

↬ 30 = 0 + 10 × t

↬ 30 = 10 × t

↬ $\sf{\dfrac{30}{10}}$ = t

↬ t = 3s

$\overbrace{\underbrace{\sf{\red{Time = 3~seconds}}}}$

• $\sf{v^2 - u^2 = 2as}$

Substitute the given values.

↬ $\sf{(30)^2 - (0)^2 = 2 \times 10 \times s}$

↬ $\sf{900 = 20 \times s}$

↬ $\sf{\dfrac{900}{20} = s}$

↬ s = 45 m

$\overbrace{\underbrace{\sf{\red{Height = 45~m}}}}$

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Know more -

Velocity -

• It is distance travelled by a body in one second in a particular direction.
• It is a vector quantity.
• Its S.I. unit is m/s.

Acceleration -

• It is the rate of change of velocity of a body.
• It is vector quantity.
• Its S.I. unit is $\sf{m/s^2}$

Equations of motion -

First equation of motion -

• v = u + at

Second equation of motion -

• s = ut + $\sf{\dfrac{1}{2} at^2}$

Third equation of motion -

• $\sf{v^2 - u^2 = 2as}$

where,

v = Finial velocity

u = Initial velocity

a = acceleration

s = distance/displacement

t = time

Answer 2

Given :

• Initial velocity, u = 0 m/s
• Final velocity, v = 30 m/s
• Acceleration due to gravity, g = 10 m/s

To find :

• Time taken to reach the ground (t)
• Height (h)

According to the question,

Note : Here,

• Acceleration (a) = Acceleration due to gravity (g)

→ v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

→ Substituting the values,

→ 30 = 0 + 10 × t

→ 30 - 0 = 10t

→ 30 = 10t

→ 30 ÷ 10 = t

→ 3 = t

So,the time is 3 seconds.

Now,

→ v² = u² + 2as

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• s = Distance

→ Substituting the values,

→ (30)² = (0)² + 2 × 10 × s

→ 900 = 0 + 20s

→ 900 - 0 = 20s

→ 900 = 20s

→ 900 ÷ 20 = s

→ 45 = s

So,the height is 45 metres.

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