# If a ball is thrown upwards at a speed of 11.2 km/s from the balcony, 4m above the ground, how much time would it take to strike the ground at the base of

1
by ankushjaswal93

2015-10-06T23:09:47+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
There is a mistake in your question. The question should be "a ball is thrown upwards at a speed of 11.2 m/s from the balcony", not  11.2km/s. If you throw something at 11.2 km/s from earth's surface, it will never return to ground.
--------------------------------------------------------------------------------------------------

For solving the question, I am assuming upward direction as positive and ground as zero elevation.

initial velocity, u = +11.2 m/s
initial position, s₀ = +4 m
g = -9.8 m/s²  (as g acts downward.)

when the ball strikes the ground,
final position, s₁ = 0 m
displacement, s = s₁ - s₀ = 0 - 4 = -4m
let the time taken = t

Using the equation of motion,
s = ut + 1/2 gt²
⇒ -4 = 11.2×t + 1/2 × (-9.8) × t²
⇒ -4 = 11.2t - 4.9t²
⇒ 4.9t² - 11.2t -4 = 0

Solving the above equation
t = [ 11.2 + √(11.2²+4×4×4.9)]/(2×4.9) and  [ 11.2 + √(11.2²+4×4×4.9)]/(2×4.9)
⇒ t =  [ 11.2 + 14.28]/(9.8) and  [ 11.2 - 14.28 ]/(9.8)
⇒ t = 25.48/9.8 and -3.08/9.8
⇒ t = 2.6 second or -0.31 second

since time can't be negative, ignore t=-0.31s

So time taken by the ball to strike the ground is 2.6s