A shell bursts on contact with the ground and pieces from it fly in all directions with a velocity equal to 60 m s^(-1). If it is known that a man who…

Question

A shell bursts on contact with the ground and pieces from it fly in all directions with a velocity equal to 60 m s^(-1). If it is known that a man who is 180 m away is in danger for a time interval of √x seconds, then what is the value of x? [Neglect the height of the man]

MARKS Content Team · Accepted Answer

Correct answer: 72. Given, u=60 m s^(-1), R=180 m ∴ R=(u^2)/gsin⁡2θ 180=(60^2)/10sin⁡2θ ⇒ sin⁡2θ=1/2 ⇒ θ=15^o As there are always two directions of projections θ and 90^o-θ for the given range, hence two directions of projection, i.e. 15^o and 90^o-15^o, i.e. 15^o and 75^o. Let T_1 and T_2 be the times of flight in the two cases, where T_1=(2usin⁡15^o)/g and T_2=(2usin⁡75^o)/g The man is in danger for a time T_2-T_1=2u/gsin⁡75^o-sin⁡15^o =2u/g2cos⁡45^osin⁡30^o using identity, sin⁡C-sin⁡D=2 cos⁡(C+D)/2sin⁡(C-D)/2 =(2×60)/10×2×1/(√2)×1/2 =√72 s

A shell bursts on contact with the ground and pieces from it fly in all directions with a velocity equal to $60 m s^{- 1}$ . If it is known that a man who is $180 m$ away is in danger for a time interval of $\sqrt{x}$ seconds, then what is the value of $x$ ? [Neglect the height of the man]

Solution

More Motion In Two Dimensions Questions

A shell bursts on contact with the ground and pieces from it fly in all directions with a velocity equal to 60 m s-1. If it is known that a man who is 180 m away is in danger for a time interval of x seconds, then what is the value of x? [Neglect the height of the man]

Solution

More Motion In Two Dimensions Questions

A shell bursts on contact with the ground and pieces from it fly in all directions with a velocity equal to $60 m s^{- 1}$ . If it is known that a man who is $180 m$ away is in danger for a time interval of $\sqrt{x}$ seconds, then what is the value of $x$ ? [Neglect the height of the man]