An arrow is released from point A on the hill (as shown) with an initial velocit

Question

An arrow is released from point A on the hill (as shown) with an initial velocity u = 5 m/s at right angle to the slope of the hill. The hill is inclined at an angle =30° w.r.t horizontal. Find the range R of the arrow where it hits the ground (Assume the point of impact lies on the hill). Work only in the coordinate system as shown. Neglect any drag.

An arrow is released from point A on the hill (as shown) with an initial velocity u = 5 m/s at right angle to the slope of the hill. The hill is inclined at an angle theta = 30 degree w.r.i horizontal. Find the range R of the arrow where it hits the ground (Assume the point of impact lies on the hill). Work only in the coordinate system as shown. Neglect any drag.

Explanation / Answer

in the given coordinate system,

acceleration due to gravity has x-component=9.8*cos 60=4.9 m/s^2

y component=9.8*sin 60=8.487 m/s^2

if it takes time t,

to reach y=0

5*t-0.5*8.487*t^2=0

t=1.178 sec

so R=0.5*4.9*1.178^2=3.4 m

so R=3.4 m

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