A projectile is fired at an angle of 30° to the horizontal such that the vertical component of its initial velocity is 80 m s -1. Its time of flight is T Its velocity at the moment t=(T/4), has a magnitude of nearly (Take .g=10 m s -2)

Question

A projectile is fired at an angle of 30° to the horizontal such that the vertical component of its initial velocity is 80 m s -1. Its time of flight is T Its velocity at the moment t=(T/4), has a magnitude of nearly (Take .g=10 m s -2) (A) 200 m s -1 (B) 160 m s -1 (C) 144 m s -1 (D) 140 m s -1

Tardigrade Admin · Accepted Answer

Vertical component of initial velocity,

u_{y} = u sin 3 0^{\circ}

or

u = \frac{u _{y}}{s i n 3 0 ^{\circ}} = \frac{80}{( 1/2 )} = 160 m s^{- 1}

Horizontal component of initial velocity,

u_{x} = u cos 3 0^{\circ} = 160 \times \frac{3}{2} = 803 m s^{- 1}

Time of flight,

T = \frac{2 u s i n θ}{g}

= \frac{2 \times 160 \times s i n 3 0 ^{\circ}}{10} = 16 s

∴ t = \frac{T}{4} = \frac{16}{4} = 4 s

Let

v

be the velocity of the projectile at

t = \frac{T}{4}

Its horizontal and vertical components are given by

v_{x} = u_{x} = 803 m s^{- 1}

v_{y} = u_{y} - g t = 80 - 10 \times 4 = 40 m s^{- 1}

Its magnitude is given by

v = v_{x}^{2} + v_{y}^{2} = (803)^{2} + (40)^{2}

= 40 12 + 1 = 4013 \approx 144 m s^{- 1}

Q. A projectile is fired at an angle of $3 0^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80 m s^{- 1}$ . Its time of flight is T Its velocity at the moment $t = \frac{T}{4},$ has a magnitude of nearly (Take $g = 10 m s^{- 2})$

$200 m s^{- 1}$

$160 m s^{- 1}$

$144 m s^{- 1}$

$140 m s^{- 1}$

Q. A projectile is fired at an angle of 30∘ to the horizontal such that the vertical component of its initial velocity is 80ms−1. Its time of flight is T Its velocity at the moment t=4T​, has a magnitude of nearly (Take g=10ms−2)

200ms−1

160ms−1

144ms−1

140ms−1

Q. A projectile is fired at an angle of $3 0^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80 m s^{- 1}$ . Its time of flight is T Its velocity at the moment $t = \frac{T}{4},$ has a magnitude of nearly (Take $g = 10 m s^{- 2})$

$200 m s^{- 1}$

$160 m s^{- 1}$

$144 m s^{- 1}$

$140 m s^{- 1}$