MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Momentum

A 24kg proj...

Question

A $24 k g$ projectile is fired at an angle of $53^{\circ}$ above the horizontal with an initial speed of $50 m / s$ . At the highest point in its trajectory, the projectile explodes into two fragments of equal mass, the first of which fall vertically with zero initial speed. How far (in m) from the point of firing does the second fragment strike the ground? (Assume the ground is level)

Open in App

Solution

Here, $m = 24 k g, u = 50 m / s$
$v_{x} = \frac{d x}{d t} = u cos 53 \Rightarrow x = u cos 53. t . . . (1)$ and
$v_{y} = \frac{d y}{d t} = - g t + u sin 53 \Rightarrow y = - \frac{1}{2} g t^{2} + u sin 53. t . . . (2)$
At highest point, $v_{y} = 0$ , so $- g t + u sin 53 = 0 \Rightarrow t = \frac{50 sin 53}{10} = 4 s$ and from (1) $x = 50 cos 50. 4 = 120 m$
Momentum is conserved in exploration . If $v_{x}^{'}$ be the velocity of second particle , then $m v_{x} = (m / 2) v_{x}^{'} \Rightarrow v_{x}^{'} = 2 v_{x} = 2 (50 cos 53) = 60 m / s$
The total distance covered by the second fragment along x component is
$x^{'} = 60 t + x = 60 (4) + 120 = 360 m$

Suggest Corrections

thumbs-up

0

Similar questions

24 k g

projectile is fired at an angle of

53^{\circ}

above the horizontal with an initial speed of

50 m / s

. At the highest point in its trajectory, the projectile explodes into two fragments of equal mass, the first of which fall vertically with zero initial speed. How much energy in J was released during the explosion?

Q. A projectile is fired from a gun at an angle of

45^{0}

with the horizontal and with a speed of

20 m / s

relative to ground. At the highest point in its flight the projectile explodes into two fragments of equal mass. One fragment, whose initial speed is zero falls vertically. How far from the gun does the other fragment land, assuming a level terrain? take

g = 10 m / s^{2}

Q. A projectile is fired from a gun at an angle of

45^{o}

with the horizontal and with a speed of

20

m/s relative to ground. At the highest point in its flight the projectile explodes into two fragments of equal mass. One fragment comes at rest just after explosion. How far from the gun does the other fragment land, assuming a horizontal ground? Take

g = 10 m / s^{2}

Q. A projectile of mass 4 kg is fired with a velocity 4 m/s at an angle

45^{0}

with the horizontal. At the highest position in its flight, it explodes into two fragments of masses 1 kg and 3 kg. The heavier fragment falls vertically with zero initial speed. the horizontal distance between the fragments when they touch the ground is

Q. A projectle is fired from a gun at an angle

45^{o}

with a speed of m/s relative to ground. At the highest point in its flight the explodes into two fragments of equal mass. One fragment comes at rest just after explosion. How far from the gun does the other fragment land, assuming a horizontal ground? Take

g = 10 m / s^{2} ?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon