A projectile is thrown with an initial velocity (a hati+b hatj) m / s , where hati and hatj are the unit vectors along horizontal and vertical directions respectively. If the range of projectile is twice the maximum height reached by it, then

Question

A projectile is thrown with an initial velocity (a hati+b hatj) m / s , where hati and hatj are the unit vectors along horizontal and vertical directions respectively. If the range of projectile is twice the maximum height reached by it, then (A) b=(a/2) (B) b=a (C) b=2 a (D) b=4 a

Tardigrade Admin · Accepted Answer

Given initial velocity, vecu=a hati+b hatj ∴ ux=a, uy=b Time of flight, T=(2 uy/g)=(2 b/g) Maximum height, H=(uy2/2 g)=(b2/2 g) Range, R=(2 ux uy/g)=(2 a b/g) ∵ R=2 H (Given) ∴ (2 a b/g)=2 × (b2/2 g) or 2 a=b

Q. A projectile is thrown with an initial velocity $(a \hat{i} + b \hat{j}) m / s,$ where $\hat{i}$ and $\hat{j}$ are the unit vectors along horizontal and vertical directions respectively. If the range of projectile is twice the maximum height reached by it, then

$b = \frac{a}{2}$

$b = a$

$b = 2 a$

$b = 4 a$

Q. A projectile is thrown with an initial velocity (ai^+bj^​)m/s, where i^ and j^​ are the unit vectors along horizontal and vertical directions respectively. If the range of projectile is twice the maximum height reached by it, then

b=2a​

b=a

b=2a

b=4a

Given initial velocity, u=ai^+bj^​ ∴ux​=a,uy​=b Time of flight, T=g2uy​​=g2b​ Maximum height, H=2guy2​​=2gb2​ Range, R=g2ux​uy​​=g2ab​ ∵R=2H (Given) ∴g2ab​=2×2gb2​ or 2a=b

Q. A projectile is thrown with an initial velocity $(a \hat{i} + b \hat{j}) m / s,$ where $\hat{i}$ and $\hat{j}$ are the unit vectors along horizontal and vertical directions respectively. If the range of projectile is twice the maximum height reached by it, then

$b = \frac{a}{2}$

$b = a$

$b = 2 a$

$b = 4 a$