A projectile is thrown with a velocity of 20 m / s , at an angle of 60° with the horizontal. After how much time the velocity vector will make an angle of 45° with the horizontal

Question

A projectile is thrown with a velocity of 20 m / s , at an angle of 60° with the horizontal. After how much time the velocity vector will make an angle of 45° with the horizontal (A) √3 s (B) (1/√3) s (C) (√3 + 1) s (D) (√3 - 1) s

Tardigrade Admin · Accepted Answer

As the horizontal component is the same for a projectile
Let projectile velocity is

v

when particle makes angle

4 5^{\circ}

with horizontal,
hence

v = u cos θ sec ϕ = 20 cos 6 0^{\circ} sec 4 5^{\circ}

v = 20. \frac{1}{2} . 2 = 102 m / s

t = \frac{v _{y} - u _{y}}{g} = \frac{10 3 - 10}{10} = (3 - 1) s

Q. A projectile is thrown with a velocity of $20 m / s$ , at an angle of $6 0^{\circ}$ with the horizontal. After how much time the velocity vector will make an angle of $4 5^{\circ}$ with the horizontal

$3 s$

$\frac{1}{3} s$

$(3 + 1) s$

$(3 - 1) s$

Q. A projectile is thrown with a velocity of 20m/s , at an angle of 60∘ with the horizontal. After how much time the velocity vector will make an angle of 45∘ with the horizontal

3​s

3​1​s

(3​+1)s

(3​−1)s

As the horizontal component is the same for a projectile Let projectile velocity is v when particle makes angle 45∘ with horizontal, hence v=ucosθsec⁡ϕ=20cos⁡60∘sec⁡45∘ v=20.21​.2​=102​m/s t=gvy​−uy​​=10103​−10​=(3​−1)s

Q. A projectile is thrown with a velocity of $20 m / s$ , at an angle of $6 0^{\circ}$ with the horizontal. After how much time the velocity vector will make an angle of $4 5^{\circ}$ with the horizontal

$3 s$

$\frac{1}{3} s$

$(3 + 1) s$

$(3 - 1) s$