Taking X -axis along horizontal and Y -axis along vertical, with what minimum speed must a particle be projected from the origin so that it is able to pass through a given point (.30 m, 40 m.) ? Take g = 10 m s- 2

Question

Taking X -axis along horizontal and Y -axis along vertical, with what minimum speed must a particle be projected from the origin so that it is able to pass through a given point (.30 m, 40 m.) ? Take g = 10 m s- 2 (A) 60ms- 1 (B) 30 m s- 1 (C) 50ms- 1 (D) 40ms- 1

Tardigrade Admin · Accepted Answer

Using equation of trajectory for a projectile motion :

y = x t an θ - \frac{g x ^{2}}{2 u ^{2}} (1 + (t an)^{2} θ)

For the projectile to pass through (30 m, 40 m) :

40 = 30 tan α - \frac{g ( 30 ) ^{2}}{2 u ^{2}} (1 + tan^{2} α)

or

900 (t an)^{2} α - (6 u^{2} t an α) + (900 + 8 u^{2}) = 0

For real value of

α

. The discriminant of a quadratic equation

b^{2} - 4 a c \geq 0

(6 u^{2})^{2} \geq 3600 (900 + 8 u^{2})

or

(u^{4} - 800 u^{2}) \geq 9, 00, 00

or

(u^{2} - 400)^{2} \geq (2, 50, 000)

or

u^{2} - 400 \geq 500

or

u^{2} \geq 900

or

u \geq 30 m s^{- 1}

Q. Taking $X$ -axis along horizontal and $Y$ -axis along vertical, with what minimum speed must a particle be projected from the origin so that it is able to pass through a given point $(30 m, 40 m)$ ? Take $g = 10 m s^{- 2}$

$60 m s^{- 1}$

$30 m s^{- 1}$

$50 m s^{- 1}$

$40 m s^{- 1}$

Q. Taking X -axis along horizontal and Y -axis along vertical, with what minimum speed must a particle be projected from the origin so that it is able to pass through a given point (30m,40m) ? Take g=10ms−2

60ms−1

30ms−1

50ms−1

40ms−1

Q. Taking $X$ -axis along horizontal and $Y$ -axis along vertical, with what minimum speed must a particle be projected from the origin so that it is able to pass through a given point $(30 m, 40 m)$ ? Take $g = 10 m s^{- 2}$

$60 m s^{- 1}$

$30 m s^{- 1}$

$50 m s^{- 1}$

$40 m s^{- 1}$