Question

A bullet is fired straight up from a gun with a muzzle velocity of 312 m/s. Neglecting air resistance, what will be its displacement after 1.4 s? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m

Answer 1

427.196 m

Step-by-step explanation:

Given:

Initial velocity of the bullet, u = 312 m/s

Time, t = 1.4 s

Acceleration due to gravity, g = 9.8 m/s²

since the bullet is fired in the direction opposite to the direction of the acceleration due to the gravity, the acceleration will be negative

therefore,

From Newton's equation of motion

`s=ut+(1)/(2)at^2`

where,

s is the displacement

a is the acceleration

on substituting the respective values, we get

`s=312*1.4+(1)/(2)*(-9.8)*1.4^2`

or

s = 436.8 - 9.604 = 427.196 m

Answer 2

427.196 m

Step-by-step explanation:

u = Initial velocity = 312 m/s

t = Time = 1.4 s

s = Displacement

a = -9.8 m/s² (because the bullet is decelerating as the bullet is going straight up)

Equation of motion

`s=ut+(1)/(2)at^2\\\Rightarrow s=312* 1.4-(1)/(2)* 9.8* 1.4^2\\\Rightarrow s=427.196\ m`

So, Displacement at 1.4 seconds is 427.196 m