An archer standing on the ground wishes to fire an arrow through the window of a

Question

An archer standing on the ground wishes to fire an arrow through the window of a tall tower. The archer is 32.0 m below the bottom of the window, the window is 1.5 m tall, and the archer is 67.0 m from the base of the tower. The archer fires upward towards the window with a firing angle of 31 degree above the horizontal, and a firing velocity of 63.4 m/s. There is a strong tailwind, approximately equal to the arrow's horizontal velocity, so neglect air resistance. Does the arrow go through the window or not?

Explanation / Answer

in horizontal, v0x = 63.4 cos31 = 54.3 m/s

time taken to reach the window,

t = 67 / 54.3 = 1.23 sec

in vertical,

v0y = 63.4 sin31 = 32.7 m/s

ay = - 9.8 m/s^2

Applying d = v0 t + a t^2 / 2

d = (32.7 x 1.23) - (9.8 x 1.23^2 / 2 )

d = 32.75 m

and window is from 32 to 33.5 .

so arrow will go through the window. .........Ans

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