Question

${\large{\blue{➢{\underline{\red{\bf{QUESTION :}}}}}}}$
A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate :

(i) the maximum height to which it rises,
(ii) the total time it takes to return to the surface of the earth.



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Answer 1

Answer:

u=49 m/s v=0

g= -9.8 m/s

2gh-v^2-u^2 2*-9.8*h=-2401

h=122.5 m

v=u+gt

0=49+(-9.8)t -49--9.8t

t=5 sec

So Total time=5+5=10 sec

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Answer 2

Answer:

Given :-

• A ball is thrown vertically upwards with a velocity of 49 m/s.

To Find :-

• (i) the maximum height to which it rises.
• (ii) the total time it takes to return to the surface of the earth.

Formula Used :-

$\bigstar$ Third Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v^2 =\: u^2 + 2gh}}}$

where,

• v = Final Velocity
• u = Initial Velocity
• g = Acceleration due to gravity
• h = Height

$\bigstar$ First Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v =\: u + gt}}}$

where,

• v = Final Velocity
• u = Initial Velocity
• g = Acceleration due to gravity
• t = Time Taken

Solution :-

✫ The maximum height to which it rises :

Given :

• Final Velocity (v) = 0 m/s
• Initial Velocity (u) = 49 m/s
• Acceleration due to gravity (g) = 9.8 m/s²

According to the question by using the formula we get,

$\implies \sf (0)^2 =\: (49)^2 + 2(- 9.8) \times h$

$\implies \sf 0 \times 0 =\: 49 \times 49 + (- 19.6) \times h$

$\implies \sf 0 =\: 2401 - 19.6 \times h$

$\implies \sf 0 - 2401 =\: - 19.6h$

$\implies \sf {\cancel{-}} 2401 =\: {\cancel{-}} 19.6h$

$\implies \sf 2401 =\: 19.6h$

$\implies \sf \dfrac{2401}{19.6} =\: h$

$\implies \sf 122.5 =\: h$

$\implies \sf\bold{\purple{h =\: 122.5\: m}}$

$\therefore$ The maximum height to which it rises is 122.5 m .

✫ The total time it takes to return to the surface of the earth :

Given :

• Final Velocity (v) = 0 m/s
• Initial Velocity (u) = 49 m/s
• Acceleration due to gravity (g) = 9.8 m/s²

According to the question by using the formula we get,

$\implies \sf 0 =\: 49 + (- 9.8) \times t$

$\implies \sf 0 - 49 =\: - 9.8t$

$\implies \sf {\cancel{-}} 49 =\: {\cancel{-}} 9.8t$

$\implies \sf 49 =\: 9.8t$

$\implies \sf \dfrac{49}{9.8} =\: t$

$\implies \sf 5 =\: t$

$\implies \sf\bold{\purple{t =\: 5\: seconds}}$

Now, we have to find the total time it takes to return to the surface of the earth :

$\leadsto \sf 2t$

$\leadsto \sf 2(5)$

$\leadsto \sf\bold{\red{10\: seconds}}$

$\therefore$ The total time it takes to return to the surface of the earth is 10 seconds.