Mr. Martin went for a shooting game, where a balloon starts ascending from the ground at a constant speed of 25 m·s⁻¹. After 5 seconds, Mr. Martin shot a bullet vertically upwards from the ground. What should be the minimum (approximate) speed of the bullet so that it may reach the balloon?

Since the balloon is going upwards with a constant speed of +25 m•s−1 (+ is a sign convention for upward speed). After 5 seconds, it will be at a height of +125 m (25 m•s−1 X 5 s). Now after 5 seconds let say, the bullet is shot with a speed of +u m•s−1. Applying the concept of relative velocity, we stop the balloon at a height of +125 m. We reverses its speed = (-25 m•s−1) and add into the speed of the bullet. Now speed of bullet becomes, (u - 25) m•s−1 The distance, bullet has to travel = +125 m Applying the equation,v2-u2 = 2gS , v is the final speed of the bullet = 0 m•s−1 (As it just reaches the balloon and stops), Initial Speed (u) = (u-25) m•s−1, S=+125 m, g = -10 m•s−2 (- because g always acts in the downward direction) Solving the equation,(0)2- (u-25)2 = 2 X (-10)X (+125)-(u-25)2 = - (2500) Cancelling the negative sign, and taking the square root, we get u-25 = 50 u = 75 m•s−1 (Answer)