Question

1. A balloon rising vertically up with the velocity of 15m/s²releases a stone a height 100m.Calculate the time taken by stone to reach ground.​

Answer 1

Correct question :-

A balloon rising vertically up with the velocity of 15 m/s releases a stone at a height 100 m. Calculate the time taken by the stone to reach to reach ground.

Answer :-

The stone takes 6.2 seconds to reach the ground .

Explanation :-

We have :-

→ Velocity of the balloon (u) = 15 m/s

→ Height (h) = 100 m

______________________________

If we take downward direction to be postive , then we have :-

• u = -15 m/s

• g = + 10 m/s²

Putting the values in the 2nd equation of motion, we get :-

h = ut + ½gt²

⇒ 100 = -15(t) + ½ × 10 × t²

⇒ 100 = -15t + 5t²

⇒ 5t² - 15t - 100 = 0

⇒ 5(t² - 3t - 20) = 0

⇒ t² - 3t - 20 = 0

⇒ t = [3 ± √(-3)² - 4(1)(-20)]/2

⇒ t = [3 ± 9.4]/2

⇒ t = 6.2 ; t = -3.2

As time cannot be negative, so we take postive value i.e 6.2 seconds to be the answer .

Answer 2

Answer:

Time taken by the stone to reach the ground is 6.2 seconds.

Explanation:

Given :-

A ball rising vertically up with the velocity of 15m/s.

Releases a stone at a height of 100m.

To find :-

Time taken by the stone to reach the ground.

Solution :-

Initial velocity of the stone (u) = -15m/s

Displacement (S) = 100m

Acceleration due to gravity (a) = 10m/s²

Using the equation of motion :-

$S=ut+\frac{1}{2}at^2$

Substituting :-

100 = -15(t) + $\frac{1}{2}\times10\times\;t^2$

100 = -15t × 5 × t²

100 = -15t × 5t²

5t² - 15t - 100 = 0

5(t² - 3t - 20) = 0

t² - 3t - 20 = 0

t = $3\±\frac{\sqrt{-3^2}-4(1)(-20) }{2}$

t = $3\±\frac{9.4}{2}$

t = 6.2 or -3.2

∴ Time taken by the stone to reach the ground is 6.2 seconds as time cannot be negative.