A particle is projected vertically upwards from ground with velocity 9 m/s. The time interval in which the particle is at a height greater than 4 m from ground is (g = 10 m/s2)
Answers
Given info : A particle is projected vertically upwards from the ground with velocity 9 m/s.
To find : the time interval in which the particle is at a height greater than 4 m from the ground is ...
solution : first we should find the time at which particle is at a height 4m from the ground.
s = 4m , u = 9m/s , a = -10m/s²
using formula, s = ut + 1/2 at²
⇒ 4 = 9t + 1/2 × -10 × t² = 9t - 5t²
⇒ 5t² - 9t + 4 = 0
⇒ 5t² - 5t - 4t + 4 = 0
⇒ t = 1, 4/5
therefore particle reaches the height 4m, at t = 4/5 sec and 1sec.
it means, particles height greater than 4 m between 4/5 and 1 sec. as you can see in fig.
so the time interval , Δt = 1 - 4/5 = 1/5 sec
therefore the time interval in which the particle is at a height greater than 4m form the ground is 1/5 sec.
