    Question

# A football is kicked at an angle θ = 45∘. It is intended that the ball lands in the back of a moving truck, which has a trunk of length L = 5 m. If the initial horizontal distance from the back of the truck to the ball, at the instant of the kick is 5 m & the truck moves directly away from the ball at velocity V = 9 m/s. What is approximate maximum & minimum velocity (in m/s) so that ball lands on the truck? (Assume the ball & back of the truck to be at the same horizontal level)

A

(16, 17)

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B

(16, 18)

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C

(15, 17)

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D

(15, 18)

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Solution

## The correct option is A (16, 17) Finding minimum velocity: In the case of minimum velocity the ball just lands on the back end of the truck which is initially 5 m away from the starting position of the ball. Suppose the ball lands after time 't'. In time t, truck would have moved the distance = (9t) m Total distance u = (9t) m = 5 m which should be the range in order to land it successfully. We know = u2sin 2θg=u2sin 90o10=(9t+5) t=2usin θg=2usin 45o10 =√210u u210=9√2u10+50 u2=9√2u+500=0 What is the solution? ax2+bx+c=0 x=−b±√b2−4ac2a {put some effort} u = 15.82 ms (approx.) For maximum velocity For the same reason, R = (5+5+9t)=(10+9t)=u2sin 2θg Where t = 2usin θg⇒ u max = 17.04 ms  Suggest Corrections  1      Related Videos   Falling Balls in Disguise
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