A rock is hurled horizontally from the top of a 55 m building and lands 145 m fr

Question

A rock is hurled horizontally from the top of a 55 m building and lands 145 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the top of the building, with positive y upwards and positive xin the direction of the throw.

a) How long is the rock in the air in seconds.

b) What must have been the initial horizontal componant of the velocity, in meters per second?

c) What is the vertical component of the velocity just before the rock hits the ground, in meters per second?

d) What is the magnitude of the velocity of the rock just before it hits the ground, in meters per second?

Explanation / Answer

initial position (xo, yo ) = (0,55) m

final position (x,y) = (145,0) m

(a) Using y = yo + voyt + 0.5at^2

y = 0 yo = 55 m voy = 0 m/s a= -9.81 m/s^2 t =?

0 = 55 + 0 + 0.5(-9.81)t^2

t = 3.35s

(b) Time taken = Horizontal distance covered/ Horizontal speed

t = (x-xo)/vx

vx = (x-xo)/t = (145 - 0)/3.35 = 43.28 m/s

(c) vy = voy + at

vy = 0 + (-9.81)(3.35) = -32.86 m/s

(d) v = (vx^2 + vy^2)^1/2 = ( 43.28^2 + 32.86^2)^1/2 = 54.34 m/s

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