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Question

The height y and the distance x along the horizontal plane of a projectile on a certain planet (assuming flat surface) with no surrounding atmosphere are given by x=6t and y=8t5t2, where x and y are in metre and time t is in second. Find the velocity in ms1 with which the body is projected. Take acceleration due to gravity g=10 m/s2

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Solution

Let the acceleration due to gravity on that planet be g
ux=ucosθ
uy=usinθ
x=uxt+12axt2
x=uxt (since horizontal acceleration is zero)
y=uyt+12ayt2
Putting ay=g
y=uyt12gt2
Comparing with the given data
x=6t and y=8t5t2

ux=6 and uy=8
u2=62+82
u=10 m/s

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