Question

A ball is thrown in a vertically upward direction with a velocity of 10 m/s. If the acceleration of the ball during its motion is 10 m /s2in the downward direction: a) What will be the height attained by the ball? b)How much time will it take to reach there? please give detailed answers

Answer 1

Answer:

Given, initial velocity, u=5ms

−1

Final velocity, v=0

Since, u is upward & a is downward, it is a retarded motion.

∴a=−10ms

−2

Height attained by ball, s=?

Time take to attain height, t=?

(i) Using the relation, v

2

−u

2

=2as, we have

s=v

2

−u

2

/2a

=(0)

2

−(5)

2

/2×(−10)=1.25m

(ii) Using the relation, v=u+at

0=5+(−10)t or

t=5/10=0.5s

Answer 2

GivEn:

• A ball is thrown in a vertically upward direction with a velocity of 10 m/s.

• Acceleration of ball = 10m/s²

⠀⠀⠀⠀⠀⠀⠀

To find:

• What will be the height attained by the ball?

• How much time will it take to reach there?

⠀⠀⠀⠀⠀⠀⠀

SoluTion:

Here,

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

⠀⠀⠀⠀⠀⠀⠀

★ Now, Using 1st equation of motion,

⠀⠀⠀⠀⠀⠀⠀

$\star\;{\boxed{\bf{\purple{v = u + at}}}}$

⠀⠀⠀⠀⠀⠀⠀

$\;\;\small\sf \underline{Now,\;Put\;the\;givEn\;values\;:}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 0 = 10 + ( - 10)t$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf ( - 10)t = - 10$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf -10t = - 10$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf t = \cancel{ \dfrac{-10}{-10}}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies{\underline{\boxed{\sf{\pink{t = 1\;s}}}}}\;\bigstar$

⠀⠀⠀⠀⠀⠀⠀

$\therefore$ Time taken is 1 second.

━━━━━━━━━━━━━━━━

★ Now, Again Using 3rd equation of motion,

⠀⠀⠀⠀⠀⠀⠀

$\star\;{\boxed{\bf{\purple{v^2 - u^2 = 2as}}}}$

⠀⠀⠀⠀⠀⠀⠀

$\;\;\small\sf \underline{Now,\;Put\;the\;givEn\;values\;:}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf (0)^2 - (10)^2 = 2 \times ( - 10) \times s$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 0 - 100 = - 20s$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf - 100 = -20s$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf s = \cancel{ \dfrac{ -100}{- 20}}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies{\underline{\boxed{\sf{\pink{s = 5\;m/s}}}}}\;\bigstar$

⠀⠀⠀⠀⠀⠀⠀

$\therefore$ Height attained by ball is 5 m.

━━━━━━━━━━━━━━━━━

Additional Information:-

★ There are three equations of motion:-

⠀⠀⠀✩ $\sf v = u + at$

⠀⠀⠀✩ $\sf s = ut + \dfrac{1}{2} at^2$

⠀⠀⠀✩ $\sf v^2 - u^2 = 2as$

⠀⠀ ━━━━━━━━━━━━━━━━━━━━━

$\;\;\star\;\sf Acceleration (a) = \dfrac{Final\; velocity (v) - Initial\; velocity (u)}{Time (t)}$