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Horizontal Component
The horizontal component of the velocity is constant as it is perpendicular to g.
So we can write:
vcos30=20t
Where t is the time of flight.
∴v×0.866=20t
t=200.866v (1)
Vertical Component
We can use:
s=ut+12at2
This becomes:
5=vsin30t−12gt2
∴5=v×0.5×t−12×9.8×t2
5=v×0.5×t−4.9t2 (2)
We can substitute the value of t from (1) into the first part of (2)⇒
∴5=v×0.5×200.866v−4.9t2
∴5=100.866−4.9t2
4.9t2=11.547−5=6.547
4.9t2=6.547
t2=6.5474.9=1.336
t=√1.336=1.156xs
We can now put this value of t back into (1)⇒
200.866v=t
∴0.866v=20t=201.156
∴v=201.156×0.866=19.97xm/s
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