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)

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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

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