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M2 Past Paper Question

1) A particle P is projected with velocity (2ui+3uj) m/s from a point O on a horizontal plane, where i and j are horizontal and vertical unit vectors respectively. The particle P strikes the plane at the point A which is 735m from O.

a) Show that u=24.5

b) Find the time of flight from O to A.

The particle P passes through a point B with speed 65 m/s.

c) Find the height of B above the horizontal plane.

Cheers :wink:

Reply 1

yazan_l

a) speed(horizontal) = distance / time
time to reach plane again = 735/2u
time to reach highest point = 1/2 ( 735/2u )

Uvertical = 3u
Vvertical = 0
t = 1/2 ( 735/2u )
a = -g

a = (V-U)/t

-g = -3u / (183.75/u)
u² = 600.25
u = 24.5

b) time to reach plane again = 735/2u
T = 15 sec

speed² = 49² + (V)²
65² - 49² = V²
V : speed vertical
V² = 1824

V² = U² + 2as
1842 = 5402.25 - 2 x 9.8 x S
S = 181.6 m