Motion in a Plane

Let in is body reaches upto point A and after two more second, it reaches upto point B
Total time of ascent for a body is,
t‌ascent ‌‌=2+1=3s
t‌ascent ‌‌=‌

‌ Time of flight ‌

2

=‌

2usin‌θ

2×g

‌

usin‌θ

g

‌=3⇒usin‌45∘=30‌‌...
Horizontal component of velocity remains always constant,
u‌cos‌45∘=v‌cos‌45∘
For vertical upward motion between point O and A,
‌vy=uy−gt
‌vsin‌45∘=usin‌45∘−10×1
‌‌

v

√2

=30−10‌‌‌ from Eq. (i) ‌
‌v=20√2m∕s
Putting this value in Eq. (ii),
u‌cos‌45∘=20√2×‌

1

√2

=20
From Eq. (i) and Eq. (iii),
‌u2sin‌245∘+u2cos245∘=(30)2+(20)2
‌u2=1300
‌u=10√13m∕s