Question

Time of flight of a projectile is 10 second. Its range on a horizontal plane is 100m. Calculate the angle of projectile and velocity of projectile. (g = 9.8m/s²)

Answer 1

Answer:

Given: t = 10s

Range = 100m

Wkt, Time $T = 2usin\Theta/g$

$2usin\Theta/g = 10$

$sin\Theta = (10\times9.8)/2u = 98/2u = 49/u \rightarrow (1)$

Range $R = u2 sin2\Theta/g$

u2 sin2\Theta/g = 100

$sin2\Theta = 100\times9.8/ u2$                   $(since\quad sin2\Theta = 2 sin\Theta. cos\Theta)$

$2 sin\Theta cos\Theta = 980/u2$

$2\times 49/u cos\Theta = 980/u2$

$Cos\Theta = 980/98u = 10/u \rightarrow (2)$

$sin\Theta/cos\Theta = tan\Theta$

from (1) and (2),

$(49/u)/ (10/u) = tan\Theta$

$tan\Theta = 4.9$

$\Theta = tan^{-1} (4.9) = 78.465.$

Answer 2

Answer:

Explanation:

Given: t = 10s

Range = 100m

Wkt, Time T = 2usin\Theta/g

2usin\Theta/g = 10

sin\Theta = (10\times9.8)/2u = 98/2u = 49/u \rightarrow (1)

Range R = u2 sin2\Theta/g

u2 sin2\Theta/g = 100

sin2\Theta = 100\times9.8/ u2                   (since\quad sin2\Theta = 2 sin\Theta. cos\Theta)

2 sin\Theta cos\Theta = 980/u2

2\times 49/u cos\Theta = 980/u2

Cos\Theta = 980/98u = 10/u \rightarrow (2)

sin\Theta/cos\Theta = tan\Theta

from (1) and (2),

(49/u)/ (10/u) = tan\Theta

tan\Theta = 4.9

\Theta = tan^{-1} (4.9) = 78.465.