Question

7. A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m/s? With what velocity will it strike the ground? After what time will it strike the ground?​

Answer 1

Given:-

• Height = 20m

• Initial Velocity = 0m/s ( it was at rest )

• Acceleration due to gravity = +10m/s

To Find:-

1. The final Velocity with which it strike the ground.
2. Time it will take to strike the ground.

Formulae used:-

• v² - u² = 2as

• v = u + at

Where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• S = Height
• t = Time.

Now,

→ v² - u² = 2as

→ v² = 2 × 10 × 20

→ v² = 400

→ √v² = √400

→ v = 20m/s

Therefore, The ball will strike the ground with a velocity of 20m/s

→ v = u + at

→ 20 = 0 + 10 × t

→ 20 = 10t.

→ t = 20/10

→ t = 2s

Hence, The ball will take 2 Second to hit the ground.

Answer 2

Let us assume, the final velocity with which ball will strike the ground be ‘v’ and time it takes to strike the ground be ‘t’.

Given parameters

Initial Velocity of the ball (u) = 0

Distance or height of fall (s) = 20 m

Downward acceleration (a) = 10 m s-2

As we know

2as = v2 – u2

v2 = 2as +  u2

v2 = (2 x 10 x 20 ) + 0

v2 =  400

Final velocity of ball (v) = 20 ms-1

t = (v – u)/a

Time taken by the ball to strike (t) = (20 – 0)/10

t = 20/10

t = 2 seconds

The final velocity with which ball will strike the ground is (v) =  20 ms-1

The time it takes to strike the ground (t) = 2 seconds