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A cart is moving horizontally along a straight line with constant speed 30 ms1. A particle is to be fired vertically upwards from the moving cart in such a way that it returns to the cart at the same point from where it was projected after the cart has moved 80 m. At what speed (relative to the cart) must the projectile be fired? (Take g=10 ms1)

A
10 ms1
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B
108 ms1
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C
403 ms1
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D
None of these
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Solution

The correct option is C 403 ms1

Let the projectile be fired at speed v vertically w.r.t. cart.
Initial horizontal velocity of projectile
ux=u=30 m/s and
uy=v

Time taken for vertical journey = Time taken for horizontal journey = Time of flight (T)

2vg=xux=8030
v=80×1030×2=403 m/s

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