Question

A ball is projected in vertical plane from the ground at an angle of 30 degrees from horizontal at t is equal to 0 seconds the ball is at the same height at t is equal to 1 S and T is equal to 3 then maximum height attained by the ball is​

Answer 1

Given :

▪ Angle of projection = 30°

▪ Ball is at the same height at t = 1s and t = 3s.

To Find :

▪ Maximum height attained by the ball.

Concept :

☞ There are two values of time in projectile motion for which the projectile is at the same height. The sum of these two times is equal to the time of flight.

$\therefore$ Time of flight = 1+3 = 4s

Calculation :

✴ Initial velocity of projectile :

$\dashrightarrow\sf\:T=\dfrac{2u\sin\theta}{g}\\ \\ \dashrightarrow\sf\:4=\dfrac{2u\sin30\degree}{10}\\ \\ \dashrightarrow\sf\:40=2u\times \dfrac{1}{2}\\ \\ \dashrightarrow\bf\:u=40\:ms^{-1}\:\longrightarrow\:\bigstar$

✴ Max. height attained by ball :

$\Rightarrow\sf\:H=\dfrac{u^2\sin^2\theta}{2g}\\ \\ \Rightarrow\sf\:H=\dfrac{(40)^2\sin^2 30\degree}{2\times 10}\\ \\ \Rightarrow\sf\:H=80\times \dfrac{1}{4}\\ \\ \Rightarrow\underline{\boxed{\bf{\blue{H=20m}}}}\:\orange{\bigstar}$