Motion in a Plane

Question : 15

Total: 32

The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m s‌–1 can go without hitting the ceiling of the hall?

Solution:

Here, H = 25 m; u = 40 m s ‌–1
Suppose that the ball is thrown at an angle q with the horizontal.
We know, H=

u2sin2θ

∴25=

(40)2sin2θ

2×9.8

or sin2θ=

25×2×9.8

(40)2

or sin‌θ=√49040=0.5534 or θ=33.6°
Now, R=

u2‌sin‌2‌θ

(40)2‌sin‌2(33.6°)

9.8

(40)2‌sin‌67.2°

9.8

(40)2×0.9219

9.8

=150.5m

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