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Physics-

General

Easy

Question

A cart is moving horizontally along a straight line with constant speed $30 blank m divided by s$ . A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved $80 blank m$ . At what speed (relative to the cart) must the projectile be fired $left parenthesis$ Take $blank g equals 10 blank m divided by s to the power of 2 end exponent right parenthesis$

$10 m / s$
$10 \sqrt{8} m / s$
$\frac{40}{3} m / s$
None of these

The correct answer is: $fraction numerator 40 over denominator 3 end fraction blank m divided by s$

As seen from the cart, the projectile moves vertically upward and comes back
The time taken by cart to cover $80 blank m$
$fraction numerator s over denominator v end fraction equals fraction numerator 80 over denominator 30 end fraction equals fraction numerator 8 over denominator 3 end fraction blank s$
For a projectile going upward , $a equals negative g equals negative 10 blank m divided by s to the power of 2 end exponent comma blank upsilon equals 0$
And $t equals fraction numerator 8 divided by 3 over denominator 2 end fraction equals fraction numerator 4 over denominator 3 end fraction blank s$
$therefore upsilon equals plus a blank t rightwards double arrow 0 equals u minus 10 cross times fraction numerator 4 over denominator 3 end fraction rightwards double arrow u equals fraction numerator 40 over denominator 3 end fraction blank m s to the power of negative 1 end exponent$

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