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Question

A projectile is fired horizontally with a speed of 98 ms−1 from the top of a hill 490 m high. Find
(i) The time taken to reach the ground
(ii)The distance of the target from the hill and
(iii)The velocity with which the projectile hits the ground. (take g=9.8 m/s2)

A
(i) 5 s, (ii) 490 m, (iii) 110 m/s
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B
(i) 10 s, (ii) 980 m, (iii) 982 m/s
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C
(i) 15 s, (ii) 1470 m, (iii) 110 m/s
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D
(i) 5 s, (ii) 980 m, (iii) 98 m/s
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Solution

The correct option is B (i) 10 s, (ii) 980 m, (iii) 982 m/s


(i) The projectile is fired from the top 0 of a hill with speed ux=98 ms1 and uy=0 along the horizontal as shown. It reaches the target P at vertical depth OA, in the coordinate system as shown.
OA=y=490 m
From second equation of motion,
y=uyt+12gt2=12gt2
490=12×9.8t2
t=100=10 s

(ii) Distance of the target from the hill is given by
AP=x=Horizontal velocity×time=98×10=980 m

(iii) The horizontal and vertical components of velocity v of the projectile at point P are
vx=u=98 ms1
vy=uy+gt=0+9.8×10=98 ms1
v=v2x+v2y=982+982=982 ms1

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