A ball is thrown vertically upward from ground with a speed of 24 5 ms

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

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

Answer»

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.