Question

A stone is thrown in a vertically upward direction with a velocity of 5m/s . If the acceleration of the stone during its motion 10m/s in the downward direction , what will be the height attained by the stone and how much time will it take to reach there ?​

Answer 1

Answer:-

h = 1.25 m

t = 0.5 s

Given:-

u = 5m/s

g = 10m/s²

v = 0 m/s

To find :-

The maximum height reached.

Time take to reach their.

Solution:-

During an upward motion the final velocity (v)of the body become 0.

Now, first we have to calculate

first we have to calculateMaximum height:-

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

From, equation of motion under the influence of gravity.

→$h_{max} = \dfrac{5^2}{2\times10}$

→$h_{max}= \dfrac{25}{20}$

→$h_{max}= 1.25 m$

Now,

we have to calculate time of ascent I.e, time to reach maximum height.

The formula for time of ascent is given by :-

★ $\boxed{\sf{t_a = \dfrac{u}{g}}}$

Put the given value,

→$t_a = \dfrac{5}{10}$

→$t_a = 0.5s$

hence,

The maximum height reached by stone is 1.25 m and time taken to reach is 0.5s.

Answer 2

Answer:

Maximum height = 1.25 m

Time taken = 0.5 seconds

Explanation:

given that,

A stone is thrown in a vertically upward direction with a velocity of 5m/s

here,

we have,

initial velocity of the stone = 5 m/s

gravitational acceleration = 10 m/s²

let the maximum height that the stone can attain be h

so,

final velocity at h = 0 m/s [stone will stop at the maximum height}

now,

we have,

initial velocity(u) = 5 m/s

final velocity(v) = 0 m/s

gravitational acceleration(g) = -10 m/s² [against the gravitational force]

so

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 = 1.25 m

now,

we have,

initial velocity(u) = 5 m/s²

gravitational acceleration(g) = -10 m/s²

so,

by the gravitational equation of motion,

v = u + gt

putting the values,

0 = 5 + (-10)t

-10t + 5 = 0

-10t = -5

t = -5/-10

t = 1/2

t = 0.5 seconds

so,

time taken by the stone to reach the maximum height

= 0.5 seconds

_______________

Maximum height = 1.25 m

Maximum height = 1.25 mtime taken = 0.5 seconds