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3-2.Motion in Plane
hard
A cart is moving horizontally along a straight line with a constant speed of $30\,m / s$. A projectile is to be fired from the moving cart in such a way that it will retum to the cart (at the same point on cart) after the cart has moved $80\,m$. At what velocity (relative to the cart) must be projectile be fired? (Take $=10\,m / s ^2$ )
A
$10\,m/s$
B
$\frac{20}{3}\,m/s$
C
$\frac{40}{3}\,m/s$
D
$\frac{80}{3}\,m/s$
Solution
(c)
The time taken by cart to cover $80\,m$
$\frac{s}{v}=\frac{80}{30}=\frac{8}{3}\,s$
The projectile must be fired (relative to cart) vertically upwards.
$a=-g=-10\,ms ^2, v^s=0 \text { and } t=\frac{8 / 3}{2}=\frac{4}{3}\,s$
$\therefore v^{\prime}=u+a t \text { or } 0=u-10 \times \frac{4}{3}$
$\text { or } u=\frac{40}{3}\,ms ^{-1}$
Standard 11
Physics
