A particle is projected under gravity (g=9.81 m/s2) with a velocity of 29.43 m/s at an elevation of 30o . The time of flight in seconds to a height of 9.81 m are

Question

A particle is projected under gravity (g=9.81 m/s2) with a velocity of 29.43 m/s at an elevation of 30o . The time of flight in seconds to a height of 9.81 m are (A)  1, 2  (B)  5, 1.5  (C)  1.5, 2  (D)  2, 3

Tardigrade Admin · Accepted Answer

For the vertical motion, 9.81=29.43 sin 30o-(1/2)× 9.81× t2 [∵ Vertical displacement =(u sin α )t-(1/2)gt2] ⇒ 1=3 sin 30ot-(t2/2) ⇒ t2-3t+2=0 ⇒ t=1, 2

Q. A particle is projected under gravity $(g = 9.81 m / s^{2})$ with a velocity of $29.43 m / s$ at an elevation of $30^{o}$ . The time of flight in seconds to a height of $9.81 m$ are

$1, 2$

$5, 1.5$

$1.5, 2$

$2, 3$

For the vertical motion,
$9.81 = 29.43 sin 30^{o} - \frac{1}{2} \times 9.81 \times t^{2}$
$[∵$ Vertical displacement $= (u sin α) t - \frac{1}{2} g t^{2}]$
$\Rightarrow$ $1 = 3 sin 30^{o} t - \frac{t ^{2}}{2}$
$\Rightarrow$ $t^{2} - 3 t + 2 = 0$
$\Rightarrow$ $t = 1, 2$

Q. A particle is projected under gravity (g=9.81m/s2) with a velocity of 29.43m/s at an elevation of 30o . The time of flight in seconds to a height of 9.81m are

1,2

5,1.5

1.5,2

2,3