Question

A stone is thrown vertically up wards direction with a velocity of 5 meter per second if the acceleration of the stone in motion is 10 metre per second square in the downward direction what will be highs attained by the stone and how much time will it take to reach there

Answer 1

Answer:

➪ maximum height reached by stone

= 1.25 meter

➪ time taken to reach maximum height

= 0.5 seconds

Step by step explanations :

given that,

A stone is thrown vertically up wards direction with a velocity of 5 m/s

here,

initial velocity of the stone = 5 m/s

and

acceleration of the stone = 10 m/s²

since acceleration is in the downward direction so,

acceleration will negative

and

acceleration = -10 m/s²

let the maximum height reached by the stone = h

and time taken to reach the maximum height = t

here,

final velocity of the stone = 0 m/s

[because stone will be at rest at its maximum height ]

now

we have

initial velocity(u) = 5 m/s

final velocity(v) = 0 m/s

acceleration(g) = -10 m/s²

height(h) = h

time taken = t

by the gravitational equation of motion,

v² = u² + 2gh

putting the values,

(0)² = (5)² + 2(-10)h

-20h + 25 = 0

-20h = -25

h = -25/-20

h = 5/4

h = 1.25 m

so,

maximum height reached by stone

= 1.25 meter

now,

also

v = u + gt

putting the values,

0 = 5 + (-10)t

-10t = -5

-10t = -5

t = -5/-10

t = 5/10

t = 1/2

t = 0.5 s

so,

time taken to reach maximum height

= 0.5 seconds

__________________

➪ maximum height reached by stone

= 1.25 meter

➪ time taken to reach maximum height

= 0.5 seconds

Answer 2

Answer :-

$\mathsf{h_{max} = 1.25 m}$

$\mathsf{t = 0.5 s}$

Given :-

u = 5 m/s

g = 10 m/s

v = 0 m/s

To find :-

The maximum height attained and time of asscend.

Solution:-

Let it attained maximum height h in time t.

Then,

by using equation of motion under the influence of gravity.

Maximum height reached by the stone is given by :-

$\huge \boxed{h_{max}= \dfrac{u^2}{2g}}$

Put the given values,

→$\mathsf{h_{max} = \dfrac{(5)^2}{2 \times 10}}$

→$\mathsf{h_{max} = \dfrac{25}{20}}$

→$\mathsf{h_{max} = 1.25 m}$

hence,

The maximum height reached by the stone will be 1.25 m.

Time taken to reach the maximum height also known as time of asscend is given by :-

→$\huge \boxed{t = \dfrac{u}{g}}$

→$\mathsf{t = \dfrac{5}{10}}$

→$\mathsf{t = 0.5 s}$

hence,

Time taken by the stone to reach the maximum height is 0.5 s.