Question

car in 12 s, since it started from the rest ?
Two balls are thrown vertically upwards simultaneously with initial velocities 10 m/s and 20 m/s
respectively. Find the ratio of heights attained by the two balls.​

Answer 1

Answer:

Since the first part of the question seems misleading, I'm answering the second alone.

The Maximum height is attained when the final velocity of the ball reaches zero. By using the first equation of motion (v = u + at) we can find the time taken in reaching the maximum height. Then we can apply the second equation of motion (s = ut + 0.5at²) to calculate the height.

Case 1: Ball with u = 10 m/s

Applying 1st equation of motion,

→ v = u + at

→ 0 = 10 + (-10)t

→ -10 = -10t

→ t = 1 second

Hence this ball takes 1 second to reach the maximum height. Applying the 2nd equation we get:

→ s = ut + 0.5 at^2

→ s = 10 ( 1 ) + 0.5 ( -10 ) ( 1² )

→ s = 10 - 5

→ s = 5 m

Hence this ball reaches a height of 5 m.

Case 2: Ball with u = 20 m/s

Applying the 1st equation of motion

→ v = u + at

→ 0 = 20 + (-10)t

→ -20 = -10t

→ t = 2 seconds

Hence this ball takes 2 seconds to reach the maximum height. Applying the 2nd equation we get:

→ s = ut + 0.5 at²

→ s = 20 ( 2 ) + 0.5 ( -10 ) 2²

→ s = 40 - 20 = 20 m

Hence this ball reaches a height of 20 m.

$\boxed{ \text{Ratio of height} = \dfrac{5}{20} = \dfrac{1}{4}}$