Question

An object is thrown vertically upwards with a velocity of 20 ms-1. find
(1)the distance travelled by the object to reach the highest point.
(2)the time taken by the object to reach the highest point.
(take g=10m-1)​​

Answer 1

Given :

• Initial velocity (u) = 20 m/s
• Final velocity (v) = 0 m/s
• Acceleration (a) = - 10 m/s²

To Find :

• Distance travelled by object to reach the highest point.
• Time taken to reach highest point.

Solution :

The body is thrown vertically upwards with velocity of 20 m/s , it means initial velocity is 20 m/s. And if it is thrown upwards it will come to rest, So, final velocity is 0 m/s. The gravitational force is applied on the opposite direction of motion, so we will took acceleration is - 10 m/s².

We have to use equations of Motion, here two equations would be used. 1st and 3rd equation of motion.

$\bigstar \: \: \boxed{\sf{v \: = \: u \: + \: at}} \\ \\ \bigstar \: \: \boxed{\sf{v^2 \: - \: u^2 \: = \: 2as}}$

Where,

• v is final velocity.
• u is initial velocity.
• t is time interval.
• a is acceleration.
• s is distance.

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First, we will calculate the time taken to reach maximum height using 1st equation of motion.

$\implies \sf{v \: = \: u \: + \: at} \\ \\ \implies \sf{v \: - \: u \: = \: at} \\ \\ \implies \sf{0 \: - \: 20 \: = \: -10t} \\ \\ \implies \sf{-20 \: = \: -10t} \\ \\ \implies \sf{10t \: = \: 20} \\ \\ \implies \sf{t \: = \: \dfrac{20}{10}} \\ \\ \implies \sf{t \: = \: 2}$

$\therefore$ Time taken to reach maximum height is 2 seconds.

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Now, we will calculate the distance travelled by the body, using 3rd equation of motion.

$\implies \sf{v^2 \: - \: u^2 \: = \: 2as} \\ \\ \implies \sf{0^2 \: - \: 20^2 \: = \: 2 \: \times \: -10 \: \times \: s} \\ \\ \implies \sf{-400 \: = \: -20s} \\ \\ \implies \sf{20s \: = \: 400} \\ \\ \implies \sf{s \: = \: \dfrac{400}{20}} \\ \\ \implies \sf{s \: = \: 20}$

$\therefore$ Distance travelled by object is 20 m

Answer 2

Answer:

Explanation:

Solution,

Here, we have,

Initial velocity of object, u = 20 m/s

Final velocity of object, v = 0

Acceleration, g = 10 m/s

To find,

1. Distance traveled, s = ?

2. Time taken, t = ?

1. Distance traveled, s

We know that,

3rd equation of motion,

i.e v² - u² = 2(- g)s

⇒ (0)² - (20)² = 2 × (- 10) × s

⇒ 400 = 20s

⇒ 400/20 = s

⇒ s = 20 m

Hence, the distance traveled by object is 20 m.

Now, 2. Time taken, t

We know that,

1st equation of motion

i.e v = u + (- g)t

⇒ 0 = 20 + (- 10) × t

⇒ 20 = 10t

⇒ 20/10 = t

⇒ t = 2 seconds

Hence, the time taken by object is 2 seconds.