Question

Due to flow of wind only the range of the projectile is increased by 40% of its maximum height The acceleration of the wind in s. I unit is

Answer 1

Answer:

Due to flow of wind only the range of the projectile is increased by 40% of its maximum height The acceleration of the wind in s. I unit is

Answer 2

The acceleration due to wind is 0.1 $m/s^2$.

Given,

A projectile in which due to the flow of wind, the range of the projectile increases by 40%.

To find,

The acceleration of the wind, a$_w$.

Solution,

Let, initial velocity = u, angle of flight = θ , range without wind = R, range with the with = R', the time of flight = T, and maximum height = H$_{max$.

We know, that when not affected by the wind,

H$_{max$ = $u^2sin^2$θ/2g

R = $u^2sin2$θ/g

also according to the question,

R' = R + 40% H$_{max}$ ______ (1)

now, when the acceleration due to the wind starts

R' = ucosθT + 1/2 a$_w$$T^2$

⇒ R' = ucosθ.2usinθ/g + 1/2 (a$_w$4$u^2sin^2$θ)/g

⇒ R' = $u^2sin2$θ/g + a$_w$2$u^2sin^2$θ/g ____ (2)

From equations 1 and 2 we get,

R + 40% H$_{max}$ = R' = $u^2sin2$θ/g + a$_w$2$u^2sin^2$θ/g

⇒ $u^2sin2$θ/g + 2/5$u^2sin^2$θ/2g =  $u^2sin2$θ/g + a$_w$2$u^2sin^2$θ/g

⇒ 1/10 = a$_w$

⇒ a$_w$ = 0.1 $m/s^2$

So, the we conclude that a$_w$ = 0.1 $m/s^2$.