The angle which the velocity vector of a projectile, thrown with a velocity v , at an angle θ to the horizontal, will make with the horizontal after time t of its being thrown up is

Question

The angle which the velocity vector of a projectile, thrown with a velocity v , at an angle θ to the horizontal, will make with the horizontal after time t of its being thrown up is (A) θ  (B)  tan -1((θ/t)) (C)  tan -1((v cos θ/v sin θ- mathrmg t)) (D)  tan -1((v sin θ- mathrmg t/v cos θ))

Tardigrade Admin · Accepted Answer

velocity at any time t, during the motion of a projectile is given as

v \to = v cos θ \hat{i} + (v s in θ - g t) \hat{j}

∴

t an α = \frac{v _{y}}{v _{x}} = \frac{v s in θ - g t}{v cos θ}

Q. The angle which the velocity vector of a projectile, thrown with a velocity $v$ , at an angle $θ$ to the horizontal, will make with the horizontal after time $t$ of its being thrown up is

$θ$

$tan^{- 1} (\frac{θ}{t})$

$tan^{- 1} (\frac{v c o s θ}{v s i n θ - g t})$

$tan^{- 1} (\frac{v s i n θ - g t}{v c o s θ})$

velocity at any time t, during the motion of a projectile is given as
$v \to = v cos θ \hat{i} + (v s in θ - g t) \hat{j}$
$∴$ $t an α = \frac{v _{y}}{v _{x}} = \frac{v s in θ - g t}{v cos θ}$

Q. The angle which the velocity vector of a projectile, thrown with a velocity v , at an angle θ to the horizontal, will make with the horizontal after time t of its being thrown up is

θ

tan−1(tθ​)

tan−1(vsinθ−gtvcosθ​)

tan−1(vcosθvsinθ−gt​)

velocity at any time t, during the motion of a projectile is given as v→=vcosθi^+(vsinθ−gt)j^​ ∴ tanα=vx​vy​​=vcosθvsinθ−gt​

Q. The angle which the velocity vector of a projectile, thrown with a velocity $v$ , at an angle $θ$ to the horizontal, will make with the horizontal after time $t$ of its being thrown up is

$θ$

$tan^{- 1} (\frac{θ}{t})$

$tan^{- 1} (\frac{v c o s θ}{v s i n θ - g t})$

$tan^{- 1} (\frac{v s i n θ - g t}{v c o s θ})$

velocity at any time t, during the motion of a projectile is given as
$v \to = v cos θ \hat{i} + (v s in θ - g t) \hat{j}$
$∴$ $t an α = \frac{v _{y}}{v _{x}} = \frac{v s in θ - g t}{v cos θ}$