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A gun in a hovering helicopter fires a bullet with an initial velocity of 100 m/

ID: 1655448 • Letter: A

Question

A gun in a hovering helicopter fires a bullet with an initial velocity of 100 m/s at an angle of 37 degrees below the horizontal. The bullet hits the ground 2 seconds later.

a) Find the horizontal (x) and vertical (y) components of the bullet's inital velocity

b) How far does the bullet travel in the horizontal direction before it lands?

c) How high above the (level) ground was the plane when the bullet was fired?

d) Find the magnitude of the velocity of the bullet right before it hits the gound

Explanation / Answer

here,

the initial speed , u = 100 m/s

theta = 37 degree

a)

the horizontal component of velocity , ux = u * cos(theta)

ux = 100 * cos(37) = 79.86 m/s

the vertical component of velocity , uy = u * sin(theta)

uy = 100 * sin(37) = 60.2 m/s

b)

the horizontal distance travelled , x = ux * t

x = 79.86 * 2 = 159.7 m

c)

the height above the level ground , h = uy * t = 60.2 * 2 = 120.4 m/s

d)

final vertical speed , v = uy + g * t

v = 60.2 + 9.81 * 2

v = 79.82 m/s

the magnitude of velocity of bullet , v = sqrt(79.82^2 + 79.86^2)

v = 112.9 m/s

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