A ball is thrown vertically upward
with velocity 20 m/s from a rail road
car moving with a velocity 5 m/s
horizontally. A person standing on the
ground observes its motion as projectile.
Find maximum height attained by the
ball if point of projection is at a height
3 m from the ground.
A body is projected at time t = 0 from a
certain point on a planet surface with
a certain velocity at a certain angle
with the planet′s surface (assumed
horizontal). The horizontal and vertical
displacement x and y in metre are
related to time as x = 10(√3)t and
y = 10t − 4t^2 . Find vertical component
of velocity of the particle when it is at a
height half of the maximum height
attained.
A man observes that when he moves up
a distance c metres on a slope, the
angle of depression of a point on the
horizontal plane from the base of the
slope is 30°, and when he moves up
further a distance c metres, the angle of
depression of that point is 45°. The
angle of inclination of the slope with the
horizontal is?
Each side of an equilateral triangle
subtends angle of 60° at the top of a
tower of height h standing at the centre
of the triangle. If 2a be the length of the
side of the triangle, then (a^2 /h^2 ) = ?
If a flagstaff subtends equal angles at 4
points A, B, C and D on the horizontal
plane through the foot of the flagstaff,
then A, B, C and D must be the
vertices of
(1) Square
(2) Cyclic quadrilateral
(3) Rectangle
(4) Parallelogram
A grasshopper can jump a maximum
horizontal distance of 40 cm. If it
spends negligible time on the ground
then in this case its speed along the
horizontal road will be?
If a^→ , b^→ , c^→ are mutually perpendicular
vectors of equal magnitudes, show that
the vector a^→ + b^→ + c^→ is equally inclined
to a^→ , b^→ and c^→ .
Let a^→ = i^∧ + 4j^∧ + 2k^∧ , b^→ = 3i^∧ − 2j^∧ + 7k^∧
and c^→ = 2i^∧ − j^∧ + 4k^∧ . Find a vector d^→
which is perpendicular to both a^→ and b^→ ,
and c^→ ∙ d^→ = 15.