Question

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location 2 where g = 10.0 m/s . The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. What is the initial velocity of the bullet?

Answer 1

Given that

g = 10 m/s^2

initial x component of velocity Vx = ucos = 86.6 m/s^2-----------(1)

initial y component of velocity Vy = usin = 50 m/s^2------------(2)

from (1)and (2)

Vx^2+Vy^2 = u^2(cos^2+sin^2)

Vx^2+Vy^2 = u^2

u = Sqrt(Vx^2+Vy^2 )

u = Sqrt{(86.6^2)^2+(50)^2}

u = 100 m/s

so the initial velocity of bullet will be 100 m/s

also from (1) and (2)

Vy/Vx = sin/cos = tan

= tan^-1(Vy/Vx) = tan^-1(50/86.6)

= 30 degree