Question

A ball is thrown vertically upward from ground with a speed of 24 5 ms. After what time intervals, the ball vill
be at a height of 294 m from the ground ?

Answer 1

Correct Question

A ball is thrown vertically upward from ground with a speed of 24.5 m/s. After what time intervals, the ball will be at a height of 29.4 m from the ground ?

Solution-

A ball is thrown vertically upward from ground with a speed of 24.5 m/s.

We have to find that at what time intervals, the ball will be at a height of 29.4 m from the ground.

First equation of motion:

v = u + at

Second equation of motion:

s = ut + 1/2 at²

Third equation of motion:

v² - u² = 2as

From above data we have s = 29.4 m, u = 24.5 m/s and a is -9.8 m/s² (as it is against the motion). So, using the second equation of motion i.e. s = ut + 1/2 at²

Substitute the known values in the above formula,

→ 29.4 = 24.5(t) + 1/2 (-9.8)t²

→ 29.4 = 24.5t - 4.9t²

→ 4.9t² - 24.5t + 29.4 = 0

→ t² - 5t + 6 = 0

→ t² - 3t - 2t + 6 = 0

→ t(t - 3) -2(t - 3) = 0

→ (t - 2)(t - 3) = 0

→ t = 2, 3 sec

Therefore, the time taken by the ball is 2 or 3 sec.

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \purple{Question:-}}}}}}$

A ball is thrown vertically upward from ground with a speed of 24 5 ms. After what time intervals, the ball will be at a height of 294 m from the ground ?

_______________

${ \huge{ \bold{ \underline{ \underline{ \orange{Answer:-}}}}}}$

✒Given : -

• Speed = 245ms
• Height = 294

✒To Find : -

• Time = ?

✒Formula Used : -

$\leadsto\sf{{ \small{ \bold{ \bold{ \bold{ \red{s=ut+\dfrac{1}{2}\:{at}^{2}}}}}}}}$

✒On Substituting Values : -

$\dashrightarrow\sf{29.4=24.5(t)+\dfrac{1}{2}\:(-9.8){t}^{2}}$

$\dashrightarrow\sf{29.4=24.5t-4.9{t}^{2}}$

$\dashrightarrow\sf{4.9{t}^{2}-24.5t+29.4=0}$

$\dashrightarrow\sf{{t}^{2}-5t+6=0}$

$\dashrightarrow\sf{{t}^{2}-3t-2t+6=0}$

$\dashrightarrow\sf{t(t-3)-2(t-3)-2\:(t-3)=0}$

$\dashrightarrow\sf{(t-2)\:(t-3)=0}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \green{t=2,3\sec.}}}}}}}$

Hence , Time taken by ball is 2 or 3 seconds ..