A projectile is thrown with an initial velocity of v = (pi + q hatj) m/s . If the range of the projectile is double the maximum height reached by it, then

Question

A projectile is thrown with an initial velocity of v = (pi + q hatj) m/s . If the range of the projectile is double the maximum height reached by it, then (A)  p = 2q  (B)  q = 4p  (C)  q = 2p  (D)  q = p

Tardigrade Admin · Accepted Answer

Given, v = pi + qj According to equation 2H = R (u2 sin2 θ/2g) = (u2 sin 2θ/g) sin2 θ = 2 sin θ cos θ tan θ = 2 tan θ = (q/p) ∴ 2 = (q/p) q = 2p

Q. A projectile is thrown with an initial velocity of $v = (p i + q \hat{j}) m / s$ . If the range of the projectile is double the maximum height reached by it, then

$p = 2 q$

$q = 4 p$

$q = 2 p$

$q = p$

Given, $v = p i + q j$
According to equation
$2 H = R$
$\frac{u ^{2} s i n ^{2} θ}{2 g} = \frac{u ^{2} s i n 2 θ}{g}$
$sin^{2} θ = 2 sin θ cos θ$
$tan θ = 2$
$tan θ = \frac{q}{p}$
$∴ 2 = \frac{q}{p}$
$q = 2 p$

Q. A projectile is thrown with an initial velocity of v=(pi+qj^​)m/s . If the range of the projectile is double the maximum height reached by it, then

p=2q

q=4p

q=2p

q=p