Question

14 A stone is thrown vertically upward with velocity. 30 m's calculate
(a) Time taken by stone to come back to earth after throwing
(b) Maximum height attained by the stone​

Answer 1

Answer:

time taken =9seconds

max height=45m

Explanation:

formula of max height=v^2/2g

by find h we can easily find t

formula of t=2h/g

Answer 2

GIVEN:

The velocity with which the stone is thrown represents the initial velocity of the stone.

Initial velocity , u = 30 m/s

TO FIND:

(a) Time taken by stone to come back to earth after throwing , T

(b) Maximum height attained by the stone , H

FORMULAE:

• According to first equation of motion, v = u + at.

• According to third equation of motion, v² - u² = 2as

SOLUTION:

STEP 1: To find time of flight, T

Consider the upward motion of stone:

$\implies$The velocity of the stone finally becomes zero at its maximum point.

Final velocity, v = 0

$\implies$Acceleration , a = - g

Where g is the acceleration due to gravity.

g = 10 m/s² (approximate value)

Negative sign indicates that the direction of acceleration due to gravity is opposite to the direction of its motion.

$\implies$ Let time for upward motion be t.

a = - g

v = 0

u = 30 m/s

$\implies$The first equation of motion is changed as,

v = u - gt

$0 = 30 - (10 \times t) \\ \\ - 30 = - 10 \times t \\ \\ t = \dfrac{ - 30}{ - 10} \\ \\ t = \dfrac{30}{10} \\ \\ \boxed{t = 3 \: sec}$

Time for upward motion of stone is 3 seconds.

$\implies$It is a known fact that time of upward and downward journey are same.

$\implies$Time of flight = Time of ascent + Time of descent

Time of flight = 2t

T = 2t

T = 2 × 3

$\boxed{T\: =\: 6\: seconds }$

Time taken by stone to come back to earth after throwing is 6 seconds.

STEP 2: TO FIND HEIGHT

$\implies$At the maximum height attained by the ball, its velocity is zero. ( v = 0 )

Here , s = H

a = - g

v = 0

u = 30 m/s

$\implies$The third equation of motion becomes,

v² - u² = - 2gH

${0}^{2} - {(30)}^{2} = - 2 \times 10 \times H \\ \\ - 900 = - 20 \times h \\ \\ h = \dfrac{ - 900}{ - 20} \\ \\ H = \dfrac{90 \times 10}{2 \times 10} \\ \\ H = \dfrac{90}{2} \\ \\ \boxed{H = 45 \: m}$

Maximum height attained by the stone is 45 m.

ANSWER:

• Time taken by stone to come back to earth after throwing is 6 seconds.

• Maximum height attained by the stone is 45 m.